# 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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421 views

### Understanding Boundary Condition in FEM

I am trying to understand Dirichlet and Neumann boundary conditions in FEM and I wanted to know if my inference is correct. To articulate my understanding, lets consider a simple case of TE and TM ...
200 views

### stiffness matrix for 3D regular grid in FEM

I have understood the stiffness matrix for 3D truss, and programmed Ku=f from scratch (in Java) to find the displacements. Then I moved to 3D solid but lost in too many concepts and equations, such ...
514 views

### Finite Element Analysis for Laminated Plates with Holes or Patches

As the title says, I am trying to code in FEM a plate structure that either has a hole in one of the layers or one of the layers is made of patches of plates, rather than one whole plate. However, ...
142 views

### Parallel calculation in finite elements

I am trying to solve a 1 Dimensional eigenvalue of poisson problem: $$\nabla \phi ^2 +\nabla \phi = k\phi$$ with the boundary condition: $\phi (0)=0 , \nabla \phi(1) = 0$. I could solve this ...
67 views

### Principle of virtual work - extra term needed for deformation dependent loading?

I'm working on a problem in nonlinear elasticity, for which the external forces (loadings) depend on the displacements. Following Klaus-Jürgen Bathe's book "Finite Element Procedures", the virtual ...
236 views

### FEM current toy problem

I am solving the Dirichlet problem $$\begin{cases} \Delta u = 0, \\ u|_{\partial D} = f, \end{cases}$$ in a $2d$ domain $D$ using the finite element method. What I want to get is the ...
246 views

### Resources on mesh generation for finite element methods

I know that this is not really apart of the rules as this is a recommendation question and these don't really have an answer per say. But, like this forum posting: https://stackoverflow.com/questions/...
970 views

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### Do practice and theory differ substantially when implementing Neumann Boundary Conditions using a Mixed Method?

I have implemented a pretty straightforward finite element solver for the following Poisson equation. For the purposes of this question we can assume the source term and the Dirichlet data both ...
309 views

### Lagrange multipliers space is too rich in a mathematical view

Background: Lagrange multiplier method has been employed in numerous fields, such as contact problems, material interfaces, phase transformation, stiff constraints or sliding along interfaces. It is ...
201 views

### the augmented global stiffness matrix is not positive semi-definite using Lagrange Multipliers method within FEM

The augmented global stiffness matrix is not positive semi-definite when using Lagrange Multipliers method to enforce boundary constraints on a simple square domain of integral form: I am considering ...
855 views

### Stiffness matrix computation for 4 node quadrilateral element

I am writing a finite element code for heat transfer (scalar field problem) and starting from simple 4 node quadrilateral element. I tried computing conductance (stiffness) matrix in the physical ...
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### quadratic trial functions for a 2d FEM calculation

I want to solve \begin{align} \nabla^4\psi+\alpha\nabla^2\psi+\beta\psi=F(x,y);\quad \nabla \psi\cdot \hat{n}=\nabla^3\psi\cdot \hat{n}=0\quad \text{on boundaries} \end{align} with a 2d FEM scheme. ...
2k views

### Determinant of jacobian matrix

I am using an FEM code written in Fortran which I did not design. For a particular problem, the program complains that the determinant of the Jacobian matrix is inferior to zero. I vaguely ...
128 views

### Reference Request: Raviart Thomas with hanging nodes

I am interested in reading about the analysis (existence, uniqueness, error estimates) of elliptic problems solved with a Mixed method that uses the Raviart Thomas elements (so far so good, easy to ...
2k views

### Galerkin method: Test functions vs. Basis functions

I'm a novice to finite element and I'm finding quite hard to find the actual difference between Test function(s) and Basis function(s). I would be glad if somone could explain me that and point out ...
424 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} ...
292 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. ...
180 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 ...
770 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 ...
336 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?
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### 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 ...
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### 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 ...
975 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 $P_{2} = \begin{bmatrix} 1\\2 \end{bmatrix}$: $$\int_{P_{1}}^{P_{2}} 4x + y \ ds$$...
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### 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 ...
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### 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 ...
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### 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) ...