All Questions
Tagged with pde elliptic-pde
39
questions
2
votes
2
answers
258
views
Poisson equation with discontinuous variable coefficient
Trying to solve numerically the 2D Poisson equation with variable diffusion coefficient $K$, that in general can be discontinuous.
$$ \frac{\partial}{\partial x} ( K(x,y)\frac{\partial C}{\partial x}) ...
- 445
2
votes
3
answers
153
views
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 ...
- 105
2
votes
2
answers
433
views
Semi-infinite domain transformation
Question is mostly related to literature or suggestions.
Given a semi infinite domain: $x=[0; +\infty);y=[0; +\infty)$. Willing to transform it to computational domain of: $[0,1]\times[0,1]$.
I did ...
- 362
3
votes
1
answer
97
views
"Optimal" domain partitioning in domain decomposition algorithms
When solving a PDE numerically by domain decomposition methods, what is the "optimal way" to split the domain? Are there any results stating that a particular partition of the domain yields &...
- 31
1
vote
0
answers
155
views
Solving Laplace equation with constraint on boundary
I have found the following PDE problem in a paper:
Essentially, we have a rectangular domain where there is a unknown interface $z=\xi(x)$ (liquid-air interface) separating the domain into two medium ...
- 217
2
votes
1
answer
337
views
C or fortran library to solve linear 2D/3D elliptic PDE
I am looking for a general purpose library which can solve a 2D or 3D linear elliptic PDE on a rectangular domain with mixed/Robin boundary conditions. I am a C programmer, so I would prefer a C ...
- 1,058
1
vote
0
answers
59
views
When to discretize nonlinear Poisson Equation
I am trying to solve a nonlinear poisson equation of the form:
$u_{xx} + f(u_y)u_{yy} = 0$.
In trying to get a handle on this problem, it seems like there are two approaches. I could either ...
- 121
0
votes
0
answers
78
views
Difficulty to prove the coercivity of $a(u, v)=\int_{\Omega} \nabla u \cdot \nabla v$
I'm stuck at proving the coercivity of the bilinear functional in the variational formulation of the problem:
\begin{array}{c}
-\nabla^{2} u=f \quad \text { in } \Omega \\
u=g_{D} \text { on } \...
- 145
1
vote
0
answers
106
views
Determine truncation error of PDE discretization
The equation is $$\frac{\partial}{\partial x}\left(u\frac{\partial u}{\partial x}\right)=f(x)\\ 0<x<1, u(0)=u(1)=0$$
I'm discretizing this PDE using FVM as follows:
$0=x_0=x_{1/2}<x_1<x_{...
- 226
0
votes
1
answer
348
views
Elliptic PDE finite volume method with Dirichlet boundary condition
I want to discretize the following equation using a Finite Volume Method
$$\nabla \cdot (a(x)\nabla u)=f(x)\\x\in \Omega \subset \mathbb{R}^2
\\u_{|\partial\Omega}=g$$
I'm using Voronoi cells here: ...
- 226
1
vote
0
answers
170
views
PDE discretization on triangular domain
Given the 2D Poisson equation
$$\Delta u = f\\ u(x,0) = g_1(x), 0<x<1\\u(0,y) = g_2(y), 0<y<1\\
\partial_n u (x, 1-x) =0, 0<x<1$$
defined on the domain $\Omega := \{(x,y) \in \...
- 226
1
vote
0
answers
327
views
FiPy with derivative source terms
I have a coupled nonlinear PDE system in 1 spatial dimension, in which I want to solve using FiPy. The dependent variables are $n$ and $T$:
\begin{align}
\frac{\partial n}{\partial t} \,&=\, D\,\...
- 11
0
votes
2
answers
885
views
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 ...
- 193
1
vote
1
answer
330
views
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 &\...
- 11
1
vote
1
answer
284
views
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\...
- 767