# 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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### How to apply Dirichlet and Neumann boundary condition at the corner in Finite-Element-Method?

I have a 2D rectangular domain. The governing equation on this domain is Laplace equation: ∇2f=0 In the left and right edge there is Neumann boundary conditon : ∂f∂n=a n is the normal vector to the ...
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101 views

### One dimensional $C^1$ finite elements

I tried to solve a one dimensional biharmonic equation with finite elements. I wanted to use a conforming approach (as I simply do not know a lot about other approaches) and therefore was looking for ... 64 views

### Convergence of FEM on curved boundaries, and inhomogenous boundary data

In a smooth domain in $\mathbb{R}^{2}$ or $\mathbb{R}^{3}$ let's consider $-\Delta u = f$ with $u=g$ on a part of the boundary and $\partial_\nu u = w$ on another part of the boundary, which is far ...
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### Integration of (d-1)-dimensional functions on finite element surfaces

I am trying to integrate a function $\hat u$ on the common surface of discontinuous finite elements. The function $\hat u$ lives in a $d-1$-dimensional space of functions defined on the element ...
69 views

### Convergence rate for not smooth solution with classical $P^1$ Lagrangian FEM

I'm using classical $P^1$ finite elements to solve $- \Delta u = f$ with Dirichlet BC in a 2D domain $\Omega$. I know from theory that the solution is not in $H^1$ for my particular choice of $f$, so ...
202 views

### Which way is the right way to compute the integrals in finite element methods?

Finite element methods involve integrals of functions that are not polynomials, and these integrals must be computed numerically. For example, suppose that $f$ is the right-hand side of a Poisson ...
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### Advantages of using BEM for contact problem over FEM

Are there any advantages of using BEM (Boundary Element Method) for contact problem over FEM (Finite Element Method) apart from lesser computational cost?
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249 views

### What is the difference between non-linear elastic simulation and linear elastic simulation with plasticity?

I'm learning how to do Finite Element calculations using Comsol Multiphysics. In Comsol, Linear Elastic Material and Nonlinear Elastic Material are available as material models: Using Linear Elastic ...
1 vote
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### stable solutions for Large-scale ODEs under boundary value problem

I'm doing FEM and have a problem about getting numerically stable solution for ODEs problems like: $$\frac{\mathrm{d}}{\mathrm{d}x}\mathbf{Y} = \mathbf{AY}, x\in[x_1,x_2]$$ in which $\mathbf{Y}$ ...
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### deal.II and curved faces: how can I get the curved description

I'm not a deal.II expert, and while studying step-6 I was reading the documentation of the MappingQ1 class in the deal.II documentation. At some point in the description (https://www.dealii.org/...
1 vote
126 views

### What are the prerequisites and resources to self-learn the Boundary Element Method for Contact Mechanics problems?

What are the prerequisites to learning BEM? In which order is it advisable to learn BEM and FEM - either one before the other, or does it not matter? What are some good resources to self-learn BEM? P....
278 views

### How is the surface Jacobian determinant calculated in FEM?

I am currently trying to evaluate surface forces on a structure. I came across P356 in Bathe's Finite Element Procedures 2014 (example 5.8) in which he related the edge derivative from the global to ...
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### How can I define an equipotential surface/volume in FEniCS?

I want to solve electrostatic problem for potential. Charge density and medium permittivity are known, so is the potential of a grounded surface. I know how I can implement that. But I would like to ...
1 vote
119 views

1 vote
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### What FEM solver should be used for matrix-valued FE spaces?

I am pretty new to using FE solvers. I am trying to solve a system of (up to) 9 complex equations. We write these as a matrix equation (here), (with the implied sum over $j$, for each component ...
1 vote
67 views

### Finding the weak form of a PDE with a tensor argument

I am trying to solve for the order parameter ($A$) in the Ginzburg Landau equations. I had asked on the math SE site but was recommended to ask here. We are trying to solve the following equation, (...
### A priori FEM estimates without $H^2$ regularity
In basic lectures on finite elements theory, people always assume $H^2$ regularity of the solution in order to derive $O(h^k)$ a priori estimates in the norms $H^{2-k}$, $k=1,2$. For simplicity let's ...