# Questions tagged [elliptic-pde]

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### 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 (...
1answer
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### 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 ...
0answers
469 views

### Numerical implementation of the Dirichlet-to-Neumann map

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 ...
1answer
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2answers
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### Is there a good tutorial or textbook-like source on implementing ENO/WENO with limiters in one (and more than one) dimension?

I've inherited a finite volume code that does a second-order discretization of flux terms for a set of mixed parabolic-elliptic equations with discontinuous diffusion coefficients. The impression I ...
4answers
873 views

### biharmonic equation

I want to solve the biharmonic equation numerically, that is: $$\Delta^2 u=f~~in~~\Omega$$ $$u=g_1~~on ~~\partial \Omega$$ $$\frac {\partial u}{\partial n}=g_2~~on ~~\partial \Omega$$ Using Green's ...
1answer
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### variational formulation of linear elasticity

First I'm not 100% sure I'm on the good stack for asking my question. I would like to get a bilinear form for linear elasticity that separate a rotational part from a pure divergence part, so starting ...
1answer
426 views

### Jump condition for elliptic equation in standard finite element method

Consider the elliptic PDE $-\mathrm{div}(k(x)\nabla u) = f(x) \in \Omega$ and $u = 0$ on $\partial \Omega$ If $k(x)$ is piecewise constant across an interface $\Gamma$ in the domain, then we ...
1answer
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### Points on the interface

We consider the problem $\left\{\begin{matrix} k(x)\Delta u(x)=f(x) & \text{ in } \Omega\\ u=0 & \text{ in } \Gamma \end{matrix}\right.$ where $\Omega \subset \mathbb{R}^2$ open and ...
1answer
122 views

### Calculation of error

I have written a code in which I find the approximation of the solution of this elliptic problem. I calculated the error using the following part of code: http://pastebin.com/7b5mmuRW but I get the ...