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# Questions tagged [finite-element]

A means of solving ordinary and partial differential equations. The domain of the problem is broken up into elements, and the solution in each element is expanded in a basis of functions. The Finite Element Method lends itself well to adaptive refinement, irregular geometry, and good error estimates.

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### Meshing options to generate number of the sides of and element (tetgen-triangle)

I wrote a finite element code in fortran 90. This code is really fast, except the meshing process. I used triangle and tetgen for meshing in 2D and 3D, respectively, so this process is fast, of ...
4k views

### Modern resources for learning FEM

I need to get started using Finite Element Methods. I am about to start reading Numerical solutions of partial differential equations by the finite element method by Claes Johnson, but it's dated 1987....
941 views

### Motivation behind Galerkin method

I have a question about Galerkin method. I don't understand why the Galerkin method weights the residual by the shape functions and sets it equal to zero. I want to know what is reason of this. Why we ...
35k views

### Basic explanation of shape function

I just started studying FEM in a more structured basis compared to what I used to do during my undergraduate courses. I am doing this because, despite the fact that I can use the "FEM" in commercial (...
4k views

### How to properly apply non-homogeneous Dirichlet boundary conditions with FEM?

In general, Dirichlet boundary conditions won't be satisfied exactly for FEM for non-homogeneous boundary conditions. The FEM codes I've seen set the degrees of freedom to interpolate the Dirichlet ...
8k views

### What are criteria to choose between finite-differences and finite-elements

I am used to thinking of finite-differences as a special case of finite-elements, on a very constrained grid. So what are the conditions on how to choose between Finite Difference Method (FDM) and ...
4k views

### What is the purpose of using integration by parts in deriving a weak form for FEM discretization?

When going from the strong form of a PDE to the FEM form it seems one should always do this by first stating the variational form. To do this you multiply the strong form by an element in some (...
771 views

### Computing accurate fluxes with FEM

I have solved Poisson equation on a 3d domain with neumann and dirichlet boundary condition. I get the potential, take the gradient for each element and integrate on a surface of an element, I do this ...
2k views

### The meaning of conservative discretization in Galerkin FEM and Discontinuous Galerkin

I do understand the meanning of "conservative discretization" within the FVM/FDM framework, indeed it is well explained in this post. Now, according to the table in this slide (pp.8), it concludes: ...
2k views

### PDE discretization with the method of rothe and the method of lines (Modular implementation)

The Heat equation is discretized in space with FV (or FEM), and a semi-discrete equation is obtained (system of ODEs). This approach, known as the method of lines, allows to easily switch from one ...
6k views

### What is the general idea of Nitsche's method in numerical analysis?

I know that the Nitsche's method is a very attractive methods since it allows to take into account Dirichlet type boundary conditions or contact with friction boundary conditions in a weak way without ...
5k views

### How to derive the Weak Formulation of a Partial Differential Equation for Finite Element Method?

I have taken a basic introduction to Finite Element Method, which did not emphasize a sophisticated understanding of a 'weak formulation'. I understand that with the galerkin method, we multiply both ...
1k views

### Books on mathematical foundation of finite element methods

After reading three books about finite element method, with two of them covering also finite volume and grid generation, I found myself lost when I have to discuss these topics with library developers ...
14k views

### How to formulate lumped mass matrix in FEM

When solving time dependent PDE's using the finite element method, for example say the heat equation, if we use explicit time stepping then we have to solve a linear system because of the mass matrix. ...
895 views

I am wondering how Dirichlet boundary conditions in global sparse finite element matrices are actually implemented efficiently. For example lets say that our global finite element matrix was: $$K = \... 2answers 292 views ### Stabilization of convection-dominated flow and turbulence modeling Are stabilization techniques for convection-dominated flows like SUPG+PSPG, interior penalty methods, etc. able to handle turbulent flows without tubulence model being employed, at least up to some ... 1answer 1k views ### Find the direction of the gradient on a finite element mesh Suppose we have a triangular mesh of a two dimensional shape \Omega, and on this mesh we define a P1 finite element structure. I know that given u,v by their values at the vertices of the ... 1answer 1k views ### Appropriate space for weak solutions to an elliptical pde with mixed inhomogeneous boundary conditions I'm working with the following mixed inhomogeneous boundary value problem: \nabla(\kappa\nabla u)=f in \Omega with \partial\Omega = \Omega_1 \bigcup\Omega_2 such that u=g on \partial\... 1answer 401 views ### What spatial discretizations work for incompressible flow with anisotropic boundary meshes? High Reynolds number flows produce very thin boundary layers. If wall resolution is used in Large Eddy Simulation, the aspect ratio may be on the order of 10^6. Many methods become unstable in this ... 3answers 8k views ### What is the difference between implicit FEM and explicit FEM? What is the difference between explicit FEM and implicit FEM exactly? According to the post here, it seems that the only difference is whether implicit or explicit time integration is used. As I ... 5answers 1k views ### Is discontinuous Galerkin really any more parallelizable than continuous Galerkin? I've always heard that easy parallelization was one of the advantages of DG methods, but I don't really see why any of those reasons don't also apply to continuous Galerkin. 1answer 412 views ### Finite element convergence rates for mixed problems I've coded up a Stokes Flow problem using finite elements and am in the process of verifying that it works. I'm just not sure what convergence rate I should be expecting as I globally refine the mesh. ... 3answers 432 views ### Mixed Finite Element Method for the Stokes System—Some Implementation Details I am currently working on my bachelor’s diploma. The research concerns mixed finite element method for the 2D Stokes system$$ - \Delta \boldsymbol u + \nabla p = \boldsymbol f, \quad \boldsymbol x \...
I have a 3-dimensional domain D, with 3 types of BC which I am trying to solve the Poisson equation on. $$-\nabla \cdot (\sigma(x,y,z)\nabla u)=0$$ Insulator (Neumann BC) Electrode set at some ...