# Questions tagged [elliptic-pde]

For questions about solving elliptic PDEs, a special class of second-order linear PDE in two variables.

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### Simple to program method for elliptic PDE with curved boundary?

I know very little about numerical PDE, so I apologize if this equation is ill-formed (and I appreciate any corrections). I am currently learning about Brownian motion. A classic result is that we can ...
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### Elliptic PDE finite volume method with Dirichlet boundary condition

I want to discretize the following equation using a Finite Volume Method $$\nabla \cdot (a(x)\nabla u)=f(x)\\x\in \Omega \subset \mathbb{R}^2 \\u_{|\partial\Omega}=g$$ I'm using Voronoi cells here: ...
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### Finite element method for Surface integrals using polar coordinates

I am trying to solve a 2D elliptic PDE (see complete electrode model for electrical impedance tomography) using the finite element method (FEM) over a circular region $\Omega$. I have discretized the ...
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### Are there known accuracy issues between 2D axisymmetric and 3D solutions?

In my full 3D solutions I am solving for the potential throughout a $100\times 200\times 200$ grid. Inside is a ring electrode set to -5V via a Dirichlet boundary condition, and surrounded on all ...
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### 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 ...
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### Correctly setting boundary condition for periodic linear elasticity problem

From an old, wise engineering book Peterson's Stress Concentration Factors (http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0470048247.html page 324) I've got the following problem: There is 2D ...
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1 vote
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### An example of mixed elliptic problem using lowest-order Raviart Thomas element

I try to solve the following mixed second order elliptic PDE in the domain $D=[0, 1]^2$ \begin{eqnarray*} v+\nabla p=&0 \quad &\text{in} \quad D,\\ \text{div}(v)=&1/2 \quad &\...
1 vote
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### How to correctly define the flux in a finite volume method for Poisson's equation with a piecewise constant material

How do we correctly define the flux in a finite volume method applied to Poisson's equation where we have a piecewise constant material? Specifically, say we have the equation \begin{align*} -\nabla\...
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1 vote
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### Does a mixed method solve this elliptic pde exactly if the source function is piecewise polynomial?

Let $\Omega\subset \mathbb{R}^d$, $d\in \{2,3\}$ be an open bounded polygonal/polyhedral set. Suppose I want to solve the following pde \begin{align*} \vec{q}+\vec{\nabla}u &=0\,&x&\in \...
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1 vote