# 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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### FEM 1D poisson substitution integral issue

I'm trying to solve $\begin{cases} -u''=f \\ u(0)=0 \\ u(1)= \alpha \end{cases}$ with FEM using reference elements and local coordinates. So we have the global ...
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### Method to find PDE equation coefficient satisfying mean solution?

What is the best approach to go about solving a PDE problem of the type \begin{equation} k^3\Delta u - k(\mathbf{1}\cdot\nabla u) = 0\, ,\\ u=g\; \text{on}\; \Gamma_D\, ,\\ mean(u) = u_\text{...
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### Element Preconditioner

Im just working on a preconditioner for the linear equation system $Ax = b$ arising in FEM for elliptic PDE. $A$ is a s.p.d Matrix with real valued entries. I read something about the element by ...
337 views

### Recommended visualization tools for higher order finite element solutions?

Is there any software available which can directly render higher order finite element results? In particular, 3D finite elements would be preferable. It seems gmsh has some capability in this regard ...
32 views

### Solving Compressible Euler in Primitive Variables with Galerkin P1 FEM

I have implemented a small compressible Euler solver, discretizing in primitive variables (rho, u, v, p) with standard Galerkin FEM P1 triangular elements, and mixed isotropic and anisotropic/...
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### Relation of Condition of a Matrix and Convergency

Can anybody explain me the relation between the condition of a Matrix and the convergency of a problem. For example how is the relation between the condition of the stiffness Matrix occuring in FEM ...
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### Compute outward normal and surface area for 8 noded brick element in FEA

I have a cube which is divided into 8 small cubes by bisecting each edge, I am trying to find out the surface area of each of the faces and the corresponding outward normals for them. This operation ...
260 views

### Which SciPy nonlinear solver when Jacobian is analytically known and sparse?

I have a nonlinear function fun with n inputs and n outputs. I also have a function jac which calculates the Jacobian, which is ...
66 views

### Stabilization parameter for an elliptic equation

I simply want to solve the elliptic equation: $$-\kappa \nabla^2 u + u = f$$ where $f\in [0,1]$. When using continuous Galerkin with Lagrange elements, I have noticed that $\kappa$ has to be greater ...
302 views

### Connectivity matrix in Finite Element Method in Triangular elements

Imagine a simple triangular base mesh in finite element method with an unknown number of elements (varying by the user). How can connectivity matrix be coded to be generated automatically?
148 views

### Can a second-order ODE be “inconsistent” with its boundary conditions?

I am trying to solve a set of coupled, nonlinear ODEs. The only dependent variable is a 1-dimensional spatial coordinate, let's call it $x$. For now, I've managed to approximate away some of the ...
146 views

### Does a generic method for solving a system of PDEs exist?

There are generic methods for solving systems of ODEs numerically. Are there generic methods for PDEs? If so, what are they? If not, why not? To elaborate... Any set of ODEs can be written in ...
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### How is nonlinear flux interface term assembled for Discontinuous Galerkin method for hyperbolic conservation laws?

For example, for 1D Burgers equation $$u u_x = 0 \\$$ equivalently, $$\frac{dF(u)}{dx} = 0\\ F(u)= \frac{u^2}{2}$$ If I want to obtain $A_{ij},i\ne j$ for two DOFs ($U_i$ and $U_j$) of two ...
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### How to analyze the dispersion and dissipation of a certain FEM?

In Finite Difference method or Finite volume textbook. Dispersion/Dissipation can be analyzed by set $u = u_0\exp{\omega t +\mathbf{kx}}$。 However, I cannot find something about this kind of analysis ...
213 views

### Why Coercivity is so important in FEM framework?

I know Lax-Milgram theorem is fundamental to FEM. But it did not explain what will happen if coercivity is not met. My understanding is if it is met, eigen value of the operator (or its corresponding ...
503 views

### Why is the test function space in FEM chosen with homogeneous boundary conditions?

It is so confusing, especially when I learns discontinuous galerkin method in broken Sobolev space and weak Dirichlet boundary condition. If the trial function is chosen with homogeneous boundary ...
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### Should I expect computational gains using a second-order splitting method here?

I am trying to solve a three-dimensional baroclinic transport problem. The hydrodynamic (three-dimensional shallow water) equations are: \begin{align} \nabla \cdot \vec{v} = 0, \tag{1} \\ \frac{\...
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### A reference request for computational plasticity

My background is in applied mathematics and I'm trying to learn plasticity. I have successfully understood the theory and finite element implementation of: linear elasticity, hyperelasticity (Neo-...
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### Basic approach for numerical solution of PDE

I'm looking for some guidance on how to write a program to numerically solve a PDE. As an example for comparison in 1D: $$\frac{d^2u}{dx^2} = f\;\;\;\;u(0) = 0\;\;\;\;u(1) = 0$$ We could try 6 ...
112 views

### Analytical testing/quality control for scientific software in professional setting

I am charged with maintaining a buildserver on Teamcity which is meant to test our in house FE software. Currently our test suite consists of a list of benchmarks which run every time a commit is made ...
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### Oscillation term in a posteriori error estimator

Assume that in the a (residual type) posteriori error estimator of some PDE is a term of the form $h_T\|g\|_{L^2(\Omega)}$ involved where $h_T$ is the diameter of an element and $g$ is some known data ...
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### Comparison between FEM and FDM methods for flow simulations

What are the main differences between finite element and finite difference approach for incompressible flow simulations? I have a vague idea about how FE methods rely on minimizing the residual over ...
253 views

### Influence of node numbering in a FEM problem?

In a FEM mesh, does the order of node numbering in an element has any importance? I'm currently trying to code my own FEM solver, which seems to work fine with quadrilateral elements, however I'm ...
163 views

### What is the mathematical and physical principle behind of RBE2 element？

I am writing a 3d linear finite element code to solve the standard linear elasticity equation on a tetrahedron mesh of a gearbox. Notice that, the two rectangular plates above the gearbox are fixed, ...
359 views

### How is rigid bodies implemented in finite element codes

I am writing a finite element code for structural analysis, and I want to implement rigid bodies. How is this usually done? Say that I have a square mesh, with one half of the mesh being defined rigid ...