Equation finite element course finite element analysis. Medical search. Frequent questions

Analysis and Partial Differential Equations also includes topics like calculus of variations, harmonic/wavelet analysis, and classic analysis. (siam.org)
Difference schemes for different types of partial differential equations. (ntnu.edu)
The student understands the basic theory underlying the numerical solution of partial differential equations. (ntnu.edu)
The student is able to choose suitable methods for elliptic, parabolic and hyperbolic partial differential equations. (ntnu.edu)
The student is able to set up, implement and analyze discretization methods for selected partial differential equations. (ntnu.edu)
The research focus for the Division of Numerical Analysis is on numerical methods for the solution of partial differential equations, stochastic differential equations and numerical linear algebra. (kth.se)
Finite element methods, Partial differential equations, Multiphase flow. (kth.se)
This notebook contains tests that verify that the solid mechanics partial differential equations (PDE) model works as expected. (wolfram.com)
Work on a Ph.D. thesis on "Adaptive Finite Element Methods for the Identification of Distributed Parameters in Partial Differential Equations" under the supervision of Prof. R. Rannacher (Heidelberg). (colostate.edu)
Excellent introductory text on partial differential equations with engineers in mind. (wikiversity.org)
Since the flow under consideration is a boundary layer type, the governing partial differential equations was discretized to a linear system of equations by the use of an implicit finite difference method. (global-sci.com)
R.E. Showalter, Hilbert Space Methods for Partial Differential Equations. (esaim-cocv.org)
This includes the construction, analysis, implementation and application of numerical methods for initial value problems, boundary value problems and different types of partial differential equations. (lu.se)
discretise ordinary and partial differential equations using finite difference and finite element methods and independently implement and apply such algorithms, · logically and with adequate terminology describe the construction of basic numerical methods and algorithms, · independently proceed from observation and interpretation of results to conclusion, and present and give an account of his or her conclusions on a scientific basis in a free report format. (lu.se)
Time dependent partial differential equations: numerical schemes for the diffusion equation. (lu.se)
The stochastic partial differential equation (SPDE) approach is widely used for modeling large spatial datasets. (lu.se)
Partial differential equations (PDEs) constitute one, if not the, main building block when modeling physical processes. (lu.se)

This research area includes analysis of differential equations, especially those which occur in applications in the natural sciences, such as fluid dynamics, materials science, or mathematical physics. (siam.org)
Analysis and numerical methods for differential-algebraic equations, Computational Systems Biology, Computational Neuroscience, ill-posed problems, multiscale systems. (kth.se)
The steady-state response of a dimensionless model of the mount is examined utilizing the averaging perturbation method applied to a set of second-order nonlinear ordinary differential equations. (hindawi.com)
This paper presents a new technique for solving linear Volterra integro-differential equations with boundary conditions. (projecteuclid.org)
The application of the proposed method leads the Volterra integro-differential equation to a system of algebraic equations that are easy to solve. (projecteuclid.org)
Butcher, J. C. The Numerical Analysis of Ordinary Differential Equations . (mit.edu)
Gear, C. W. Numerical Initial Value Problems in Ordinary Differential Equations . (mit.edu)
720 - Applied Mathematics I. (3) Modeling and solution techniques for differential and integral equations from sciences and engineering, including a study of boundary and initial value problems, integral equations, and eigenvalue problems using transform techniques, Green's functions, and variational principles. (sc.edu)
Basic modeling theory and solution techniques for stochastic differential equations. (sc.edu)
723 - Differential Equations. (sc.edu)
Assignments focusing on discretization methods will ensure that students are able to analyze the accuracy of a method and are able to discretize a given differential equation in space and in time. (tum.de)
Oh yes, it has some differential equations, some matrix work and some finite element analysis. (intmath.com)
These equations are in the form of a set of general differential equations. (hindawi.com)
Given that the truncated cone is divided into n disks, n sets of differential equations are obtained. (hindawi.com)
The obtained equation is an ordinary differential equation with complex coefficients. (hindawi.com)
need to solve differential equations. (pdfdrive.com)
The proposed approach is based on a pseudo‐spectral method for discretizing the differential equations and the asymptotic numerical method to convert nonlinear systems into linear algebraic equations. (wiley.com)
The coupling of the spectral method with the asymptotic numerical method is considered as an efficient algorithm to solve any nonlinear differential equations. (wiley.com)
The overarching goal of the course is that the students on completion of the course should have acquired a thorough knowledge regarding the basics of numerical analysis for differential equations. (lu.se)
independently evaluate obtained numerical results in relation to the (unknown) solution of the differential equation studied, · independently present results and conclusions of scientifically performed numerical experiments, in written or oral form, with references and other documentation of work carried out in support of their conclusions. (lu.se)

M. Feischl, T. Führer, M. Karkulik, J. M. Melenk, and D. Praetorius, Quasi-optimal convergence rates for adaptive boundary element methods with data approximation, Part II: Hyper-singular integral equation , Electron. (siam.org)
Approximation of a domain integral equation. (maa.org)
The numerical approximation of an inverse problem subject to the convection-diffusion equation when diffusion dominates is studied. (acad.ro)
We address this issue by proposing a new method based on approximating the covariance operator $L^{-2\beta}$ of the Gaussian field $u$ by a finite element method combined with a rational approximation of the fractional power. (lu.se)
Due to the sheer size of the model, the usage of direct, well-known approximation meth- ods like the Finite Element Method is not feasible and one needs to partition or split the problem. (lu.se)

Maximal $L^p$-regularity, optimal $\ell^p(L^q)$ error estimate, and $\ell^p(W^{1,q})$ estimate are established for fully discrete finite element methods with multistep backward differentiation formula. (arxiv.org)
D. Boffi, F. Brezzi and M. Fortin, Mixed Finite Element Methods and Applications. (esaim-m2an.org)
E. Colmenares and M. Neilan, Dual-mixed finite element methods for the stationary Boussinesq problem. (esaim-m2an.org)
C.I. Correa, G.N. Gatica, E. Henríquez, R. Ruiz-Baier and M. Solano, Banach spaces-based mixed finite element methods for the coupled Navier-Stokes and Poisson-Nernst-Planck equations. (esaim-m2an.org)
M. Dehghan, Z. Gharibi and R. Ruiz-Baier, Optimal error estimates of coupled and divergence-free virtual element methods for the Poisson-Nernst-Planck/Navier-Stokes equations and applications in electrochemical systems. (esaim-m2an.org)
The student masters error analysis of difference methods, and understands the concepts consistency, stability and convergence. (ntnu.edu)
The student is able to choose and apply suitable iterative methods for equation solving. (ntnu.edu)
This encompasses a wide range of methods, including finite difference, finite element and boundary integral methods, multi scale methods, Krylov methods and Monte Carlo methods. (kth.se)
We provide an abstract framework for optimal goal-oriented adaptivity for finite element methods and boundary element methods in the spirit of [C. Carstensen et al. (siam.org)
M. Aurada, M. Feischl, T. Führer, M. Karkulik, and D. Praetorius, Efficiency and optimality of some weighted-residual error estimator for adaptive 2D boundary element methods , Comput. (siam.org)
R. Becker, E. Estecahandy, and D. Trujillo, Weighted marking for goal-oriented adaptive finite element methods , SIAM J. Numer. (siam.org)
R. Becker and R. Rannacher, A feed-back approach to error control in finite element methods: Basic analysis and examples , East-West J. Numer. (siam.org)
R. Becker and R. Rannacher, An optimal control approach to a posteriori error estimation in finite element methods , Acta Numer. (siam.org)
M. Bürg and M. Nazarov, Goal-oriented adaptive finite element methods for elliptic problems revisited , J. Comput. (siam.org)
Coupled finite element/boundary element methods. (maa.org)
Inf-Sup Stable Finite Element Methods for the Landau-Lifshitz-Gilbert and Harmonic Map Heat Flow Equations. (mpg.de)
Mathematics applied to cell biology, (biophysical) models of dynamic spatial biological systems, analysis of experimental data using Bayesian model fitting methods (Markov chain Monte Carlo algorithms). (warwick.ac.uk)
Numerical analysis and scientific computing, higher order methods for solving non-linear evolution equations, generic software design for grid based numerical schemes, geophysical flows, radiation magnetohydrodynamics. (warwick.ac.uk)
Asymptotic methods in the Calculus of Variations, PDE and Stochastic Analysis (Gamma-convergence techniques, Stochastic Homogenization, Large Deviations Theory). (warwick.ac.uk)
A priori finite element error estimates are derived and an algorithm, combining the finite element and secant-modulus methods, is utilized to solve an illustrative extrusion problem. (global-sci.com)
Optimal control of the convection-diffusion equation using stabilized finite element methods. (acad.ro)
Stabilized finite element methods for nonsymmetric, noncoercive, and ill-posed problems. (acad.ro)
Solving ill-posed control problems by stabilized finite element methods: an alternative to Tikhonov regularization . (acad.ro)
Data assimilation for the heat equation using stabilized finite element methods. (acad.ro)
The use of dental implants is an excellent alternative to conventional orthodontic anchorage methods, especially in cases of a small amount or poor quality of dental elements, in the impossibility of using extraoral anchorage, or in the case of uncooperative patients 1-3 . (bvsalud.org)
The heat equations are discretized using a finite element method in space, whereas two alternative time inte- gration methods are used: implicit Euler and SDIRK2. (lu.se)

Examples of PDEs are the heat equations, the wave equation v = D2v + uv2 - ( + )v and the diffusion-reaction equation where D1, D2, and are parameters. (lu.se)

The validation of the proposed approach is made by comparison between the obtained results and those calculated using a finite element method or Ansys commercial code. (wiley.com)

The student has a basic understanding of the finite element method and iterative solution techniques for systems of equations. (ntnu.edu)
Applications in engineering and medicine, where several phys- can be seen below in contour plots of the concentration v. ical processes interact, often result in models consisting of Starting with an initial concentration consisting of four peaks large systems of equations. (lu.se)

Substitution of θ = 0 gives the explicit discretization of the unsteady conductive heat transfer equation. (wikipedia.org)
When the Péclet number (Pe) exceeds a critical value, the spurious oscillations result in space and this problem is not unique to finite elements as all other discretization techniques have the same difficulties. (wikipedia.org)
In a finite difference formulation, the spatial oscillations are reduced by a family of discretization schemes like upwind scheme. (wikipedia.org)
Themain observation of this paper is that mass conservation alone is insufficient in cases of reduced regularity and additional potential terms.In paper B we prove optimal L∞(H1)-error estimates of the Crank Nicolson discretization, both in the semi-discrete Hilbert space setting,as well as in fully-discrete finite element settings. (kth.se)
This is illustrated by numerical experiments.In Paper C we present a novel method for solving the cubic NLSE.We show that using a spatial discretization based on the method of Localized Orthogonal Decomposition, the time invariants of the equation are initially approximated to O(H6) with respect to the chosenmesh size H, while only requiring H4-regularity. (kth.se)
Finite element discretization of a Stokes-like model arising in plasma physics. (mpg.de)
Variational discretization for optimal control governed by convection dominated diffusion equations. (acad.ro)
It combines a pseudo‐spectral method for equation discretization and an asymptotic numerical method to handle non‐linear systems as linear algebraic equations. (wiley.com)

G. Bauer, V. Gravemeier and W.A. Wall, A stabilized finite element method for the numerical simulation of multi-ion transport in electrochemical systems. (esaim-m2an.org)
G.A. Benavides, S. Caucao, G.N. Gatica and A.A. Hopper, A Banach spaces-based analysis of a new mixed-primal finite element method for a coupled flow-transport problem. (esaim-m2an.org)
S. Caucao, E. Colmenares, G.N. Gatica and C. Inzunza, A Banach spaces-based fully mixed finite element method for the stationary chemotaxis-Navier-Stokes problem. (esaim-m2an.org)
E. Colmenares, G.N. Gatica and S. Moraga, A Banach spaces-based analysis of a new fully-mixed finite element method for the Boussinesq problem. (esaim-m2an.org)
G.N. Gatica, A simple introduction to the mixed finite element method, in Theory and Applications. (esaim-m2an.org)
G.N. Gatica, R. Oyarzúa, R. Ruiz-Baier and Y.D. Sobral, Banach spaces-based analysis of a fully-mixed finite element method for the steady-state model of fluidized beds. (esaim-m2an.org)
A solution of the transient convection-diffusion equation can be approximated through a finite difference approach, known as the finite difference method (FDM). (wikipedia.org)
This method is an extension of Runge-Kutta discontinuous for a convection-diffusion equation. (wikipedia.org)
The finite difference scheme has an equivalent in the finite element method (Galerkin method). (wikipedia.org)
Advanced Simulation Library Convection-diffusion equation Double diffusive convection An Album of Fluid Motion Lagrangian and Eulerian specification of the flow field Fluid simulation Finite volume method for unsteady flow "Discontinuous Finite in Fluid Dynamics and Heat transfer" by Ben Q. Li, 2006. (wikipedia.org)
The Finite Difference Method For Transient Convection Diffusion", Ewa Majchrzak & Łukasz Turchan, 2012. (wikipedia.org)
The Finite Element Method: Linear Static and Dynamic Finite Element Analysis by T. J. R. Hughes, Dover Publications, 2000. (wikiversity.org)
J. N. Reddy (1993), An Introduction to the Finite Element Method , McGraw-Hill. (wikiversity.org)
O. C. Zienkiewicz and R. L. Taylor (2000), The Finite Element Method: Volume 2 Solid Mechanics , Butterworth-Heinemann. (wikiversity.org)
Ciarlet, P. G. The Finite Element Method for Elliptic Problems . (mit.edu)
B.N. Jiang, The Least-Squares Finite Element Method: Theory and Applications in Computational Fluid Dynamics and Electromagnetics, Springer, 1998. (crossref.org)
J. M. Cascon, C. Kreuzer, R. H. Nochetto, and K. G. Siebert, Quasi-optimal convergence rate for an adaptive finite element method , SIAM J. Numer. (siam.org)
A finite element method for the 2-D solenoidal model. (maa.org)
The boundary element method for boundary integral equations. (maa.org)
In recent years, various aspects and interests in the numerical modeling of welding residual stresses and distortions, mostly using finite element method, have been elaborated by researchers. (intechopen.com)
A stabilized finite element method for inverse problems subject to the convection-diffusion equation. (acad.ro)
A stabilized finite element method is then proposed and analysed. (acad.ro)
I. Babuska, The finite element method with Lagrangian multipliers. (esaim-cocv.org)
Sundarasivarao and Ganesan [ 5 ] analyzed a conical shell under pressure using the finite element method. (hindawi.com)
The finite element method based on the Rayleigh-Ritz energy formulation is applied to obtain the elastic behavior of the functionally graded thick truncated cone [ 17 ]. (hindawi.com)
This study reviews geotechnical data relevant to the selection and design of underground mines in this region and by numerical structural analysis evaluates the importance of some geotechnical parameters to mine method selection. (cdc.gov)
The Poisson equation: finite differences and the finite element method. (lu.se)
The aim of this work is to present a high order, parallel, multirate method for two heterogeneous coupled heat equations which could be applied to FSI problems. (lu.se)
A rigorous convergence analysis of the method is performed and the accuracy of the method is investigated with numerical experiments. (lu.se)
A stable and accurate numerical method may be slow when solving the above equation due to the non-linear terms. (lu.se)

This paper investigates the existence and uniqueness of mild solutions for a class of Sobolev type fractional nonlocal abstract evolution equations in Banach spaces. (researchgate.net)
While the dependence on the scales µ and is known, via the corresponding evolution equations, the x- and bT -dependence are the subject of fitting and modeling. (lu.se)

S. Caucao and I. Yotov, A Banach space mixed formulation for the unsteady Brinkman-Forchheimer equations. (esaim-m2an.org)
A general discontinuous finite element formulation is needed. (wikipedia.org)
9 ] used the FEM for analysis of a composite conical shell where the shear deformation theory has been used for formulation. (hindawi.com)

The convection-diffusion equation describes the flow of heat, particles, or other physical quantities in situations where there is both diffusion and convection or advection. (wikipedia.org)
For information about the equation, its derivation, and its conceptual importance and consequences, see the main article convection-diffusion equation. (wikipedia.org)
In order to be concrete, this article focuses on heat flow, an important example where the convection-diffusion equation applies. (wikipedia.org)
Next, using the convection diffusion equation an equation is obtained from the differentiation of this equation. (wikipedia.org)
Unlike the conduction equation (a finite element solution is used), a numerical solution for the convection-diffusion equation has to deal with the convection part of the governing equation in addition to diffusion. (wikipedia.org)

J. Camaño, C. García and R. Oyarzúa, Analysis of a momentum conservative mixed-FEM for the stationary Navier-Stokes problem. (esaim-m2an.org)
G.N. Gatica and C. Inzunza, On the well-posedness of Banach spaces-based mixed formulations for the nearly incompressible Navier-Lamé and Stokes equations. (esaim-m2an.org)
Applications are given for the Laplace, Stokes, and Navier-Lam\'e equations. (hu-berlin.de)
This work introduces an accurate numerical approach for studying stationary incompressible Navier-Stokes equations. (wiley.com)
Abstract An accurate numerical tool is presented in this work to investigate the stationary incompressible Navier-Stokes equations. (wiley.com)

To have a more realistic modeling, utilizing nonlinear finite elements in conjunction with a lumped parameter modeling approach, we evaluate the nonlinear resorting characteristics of the components and implement them in the equations of motion. (hindawi.com)
Useful repository of information on nonlinear finite elements. (wikiversity.org)
Another excellent repository of information of nonlinear finite elements geared toward the Civil Engineers. (wikiversity.org)

K-J. Bathe (1996), Finite Element Procedures , Prentice-Hall. (wikiversity.org)

The solid mechanics equations are used to solve for the displacement of a constrained object under load. (wolfram.com)
We suggest a multirate Neumann--Neumann waveform relaxation algorithm to solve two heterogeneous coupled heat equations. (lu.se)
The main goal of this work is to describe a partitioned algo- rithm to solve two heterogeneous coupled heat equations allowing parallelization in time. (lu.se)

47 (2009), pp. 861--886] beyond the Poisson equation. (siam.org)
This paper analyzes a nonconforming 5-node quadrilateral transition finite element for Poisson equation. (global-sci.com)

We perform a one-dimensional convergence analysis for the nonmultirate fully discretized heat equations using implicit Euler to find the optimal relaxation parameter in terms of the material coefficients, the step size, and the mesh resolution. (lu.se)

Analysis of consistency, order, stability and convergence. (ntnu.edu)
Error analysis, stability and convergence. (lu.se)
Attempting to iterate Equation 2 in synchrony would not necessarily yield convergence to a local minimum - the system may wind up in a two-cycle instead, with a subset of the spins flipping signs in every update. (lu.se)

Numerical results confirm the analysis and show that the one-dimensional nonmultirate optimal relaxation parameter is a very good estima- tor for the multirate one-dimensional case and even for multirate and nonmultirate two-dimensional examples using both implicit Euler and SDIRK2. (lu.se)

A. Ern and J.-L. Guermond, Theory and Practice of Finite Elements. (esaim-m2an.org)
In this paper, Schauder fixed point theorem, Gelfand-Shilov principles combined with semigroup theory are used to prove the existence of mild and strong solutions for nonlinear fractional integrodifferential equations of Sobolev type with nonlocal conditions in Banach spaces. (researchgate.net)
Functional analysis, high-dimensional and discrete geometry, information theory. (warwick.ac.uk)
Geometric measure theory, real analysis. (warwick.ac.uk)
Group theory, groups of Lie type, finite simple groups. (warwick.ac.uk)
Theory and practice of finite elements , volume 159 of Applied Mathematical Sciences. (acad.ro)
Due to the existence of shear stress in the truncated cone, the equations governing disk layers are obtained based on first shear deformation theory (FSDT). (hindawi.com)
Most of the existing literature deals with the stress or vibration analysis of thin conical shells and is based upon a thin shell or membrane shell theory. (hindawi.com)
12 ] used the mathematical approach based on the perturbation theory, for elastic analysis of a thick conical shell with varying thickness under nonuniform internal pressure. (hindawi.com)
However, Granger and Newbold (1974) showed through Monte Carlo simulations that if the data generating process (DGP) of the variables is characterised by integration (non- stationarity), the regression analysis based on the asymptotic distribution theory does not work well and the estimated results can be spurious. (lu.se)

lution model consists of a system with approximately one hun- dred coupled 3D advection-diffusion-reaction equations (one for every trace gas concentration). (lu.se)

M. Ainsworth and J. T. Oden, A Posteriori Error Estimation in Finite Element Analysis , Pure Appl. (siam.org)

We study the well-posedness for solutions of an initial-value boundary problem on a two-dimensional space with source functions associated to nonlinear fractional diffusion equations with the Riemann-Liouville derivative and nonlinearities with memory on a two-dimensional domain. (researchgate.net)

Fictitious time-evolution for steady-state strongly non-linear transport equations. (mpg.de)

B. Jin, R. Lazarov, Z. Zhou, Two schemes for fractional diffusion and diffusion-wave equations with nonsmooth data, 2015. (crossref.org)

Residual-based a posteriori error estimates are derived wihtin a unified setting for lowest-order conforming, nonconforming, and mixed finite element schemes. (hu-berlin.de)
can be used within the proposed frame {\it without} further analysis for nonconforming or mixed FE schemes. (hu-berlin.de)

I. Babuska and M. Vogelius, Feedback and adaptive finite element solution of one-dimensional boundary value problems , Numer. (siam.org)
C. Carstensen, M. Maischak, and E. P. Stephan, A posteriori error estimate and $h$-adaptive algorithm on surfaces for Symm's integral equation , Numer. (siam.org)

The algorithm for solving the equations of the model has been discussed. (vde-verlag.de)

and development of strategies for mesh-adaptive finite element processes. (sdsmt.edu)

A central focus when numerically solving NLSEs has been to preserve the time invariants ofthese equations in the discrete setting. (kth.se)

We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit dependence on the Peclet number. (acad.ro)

In the Wolfram language, however, we use special techniques to have a higher order interpolation also in the linear element case and special algorithms to recover derivatives. (wolfram.com)

Anatomy27

Organisms1

Diseases5

Chemicals and Drugs12

Analytical, Diagnostic and Therapeutic Techniques and Equipment45

Phenomena and Processes29

Disciplines and Occupations3

Technology, Industry, Agriculture13

Information Science7

Health Care1

Partial17

Differential20

Approximation5

Methods26

Wave equation1

Calculated using a finite1

Systems of equati2

Discretization8

Method30

Evolution equations2

Formulation3

Convection-diffusion equation5

Stokes5

Nonlinear finite elements3

19961

Solve3

Poisson2

Heat equations1

Convergence3

Implicit1

Theory10

Advection-Diffusion1

Appl1

Diffusion equations1

Transport equations1

Nonsmooth data1

Schemes2

Numer2

Algorithm1

Adaptive1

Discrete1

Estimates1

Algorithms1