# 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.

843 questions
Filter by
Sorted by
Tagged with
426 views

### FEM Stiffness and Mass matrices for 2d cubic trial functions

I want to use FEM to solve a 2D eigenvalue problem for the biharmonic equation \begin{align} &K \psi= \lambda M \psi\\ &\psi=\nabla \psi\cdot \hat{n}=0\quad \text{on boundaries} \end{align} ...
303 views

### Boundary conditions for streamlines in enclosed flow

I am trying to solve Lid driven square cavity flow problem of Stokes equation using finite element method. I have boundary conditions for velocity as zeros on every boundary but u=1 on top boundary. ...
187 views

### How to precondition FEM problems using domain decomposition?

Let's say that I have a FEM code which yields the following problem: $$\mathbf{A}\mathbf{x} = \mathbf{b}.$$ In order to solve this more efficiently with an iterative method, I would like to ...
812 views

### Pressure boundary condition in lid driven cavity using finite element method

Thank you all 1.) I am trying to solve lid driven cavity problem for an incompressible Stokes and Navier Stokes equations using general "Mixed" finite element method. dirchlet boundary conditions are ...
340 views

### Imposing total pressure over surface in FEM

I am trying to solve Stokes problem using Finite element method. My question is how to impose that total pressure over the surface is zero to remove the constant pressure mode?
50 views

### Computing dilogarithm

I'm measuring the integral of a quantity which, mathematically, requires the computation of a dilogarithm function. $$\operatorname{Li}_2(be^{ax})$$ where $b$ and $a$ (are real and) can be positive ...
172 views

### FiPy: Make diffusion coefficient dependent to orientation

I'm trying to solve the heat equation in FiPy and right now it works, but I have one problem: The material I have to simulate has different diffusion coefficients in the x and y direction (due to its ...
1k views

### Line integral along the edge of an isoparametrically mapped triangle

I need to integrate the following function on the line segment from $P_{1} = \begin{bmatrix} -2\\-1 \end{bmatrix}$ to $P_{2} = \begin{bmatrix} 1\\2 \end{bmatrix}$: $$\int_{P_{1}}^{P_{2}} 4x + y \ ds$$...
97 views

### Do DG methods for the Helmholtz equation always return positive quantities?

Helmholtz Diffusion equation with reaction term: $$k\Delta u + u = f ~ \text{in} ~\Omega$$ $$\nabla u \cdot \mathbf{n} = 0 ~ \text{in} ~\partial \Omega$$ For sufficiently small $k$ (relative to ...
761 views

### Computation of stiffness matrix with variable coefficient

I am implementing a finite element solver (in 2D) to solve the generic differential equation : $$-\nabla(a(x) \nabla u) = f$$ Brief explanation By integrating and multipling by a test function, the ...
100 views

### Need clarification on a piece of book excerpt about spectral element method!

I am reading "Using MPI (3rd edition)" from William Gropp, where in chapter 4 application section 4.13, it introduces an MPI application Nek5000/NekCEM which is based on spectral element method (SEM) ...
76 views

### How to deal with multi-region problems (in PETSc)

Consider a problem where space is filled with a liquid and a solid phase, with a large, complicated geometry. On each of the phases, there's an electrical potential/poisson equation. The equations are ...
327 views

### Algebraic multigrid in PETSc

Consider a potential/poisson equation on a very large, complicated geometry. Currently, an self-written FEM and linear solvers from NumPy are used. Performance is, of course, not good enough for ...
670 views

### Eulerian vs Lagrangian vs Mesh-based vs Meshfree/Meshless methods

Hailing from the scicomp community recently getting into computer-graphics, I have noticed that the scicomp communities talk about mesh-based methods like FDM, FVM, FEM, etc, vs meshfree or meshless ...