The tag has no wiki summary.

learn more… | top users | synonyms

0
votes
1answer
54 views

jump conditions for Poisson/Darcy equation in primal form versus mixed form

Consider the Darcy equation, $$\mathbf{v} + \dfrac{k}{\mu_0}\nabla p = \mathbf{f} \\ \mathrm{div}\; \mathbf{v} = 0$$ If the coefficient $k$ is piecewise constant across an interface $\Gamma$ in the ...
2
votes
1answer
76 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 ...
4
votes
0answers
54 views

Elliptical problem with Robin BC

Working in finite differences, I am using a transformation on the temperature variable $\Theta = \int_{T0}^T \kappa(T)dT$ to linearize the steady-state heat equation into a Poisson equation ...
3
votes
2answers
124 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 ...
3
votes
1answer
48 views

Library to compute eigenvalues of the Laplace operator in a polyhedral domain

What library can one use to compute efficiently the lowest eigenvalues of the Laplace operator in a polyhedral domain in $R^3$? For the application I have in mind one has to consider very acute ...
3
votes
0answers
183 views

assembly matrices in finite element method

I'm trying to construct the right–hand side of my 2D Poisson's equation in Matlab. I used the vertex rule in order to approximate the integral: ...
5
votes
2answers
216 views

Finite element discretization of Reaction-diffusion problem with Dirac source term

I'm writing a code using continuous piecewise linear finite elements on triangular grids to solve the diffusion-reaction problem. the source function f is a Dirac mass at the center. How can i compute ...
6
votes
2answers
200 views

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 ...
11
votes
3answers
631 views

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 ...
2
votes
1answer
87 views

Solving the elliptic eigenproblem with periodic boundary conditions

Given an energy level $\mu$, I'm looking to calculate the eigenvectors corresponding to the time-independent Schrodinger operator on the torus (that is, periodic boundary conditions)-- $H = -h^2 ...
5
votes
1answer
402 views

Role of boundary conditions (e.g. periodic) in Poisson equation

Given 3D Poisson equation $$ \nabla^2 \phi(x, y, z) = f(x, y, z) $$ and the right hand side and the domain, am I free to impose any boundary conditions (BC) on the function $\phi$, or do they have to ...
3
votes
3answers
381 views

Online Poisson Solver

I'm wondering if anyone can point to a browser-based FEM (or other) 2D PDE solver for simple elliptic problems. It seem like there ought to be a javacript implementation that would allow for the ...
3
votes
1answer
122 views

Asymptotic convergence of the solution to a parabolic pde to the solution of an elliptic pde

Suppose I have the parabolic system $$u_t=\nabla\cdot(k(x)\nabla u)+f,\quad (x,t)\in\Omega\times I$$ with dirichlet boundary conditions $$u=g, \quad x\in\partial\Omega$$ and initial condition ...
3
votes
0answers
207 views

Solving PDE or eigenvalue problems without FEM

Do you know any methods/solvers for PDE or eigenvalue problems like $\begin{cases} \Delta u= 0\ (\text{ or }\lambda u) & \text{ in }\Omega \\ u =0 & \text{ on }\partial \Omega \end{cases}$ ...
2
votes
1answer
208 views

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 ...
6
votes
2answers
317 views

Helmholtz and Biharmonic equation examples with exact solution

I'm looking for examples of Helmholtz and Biharmonic equations in Cartesian co-ordinates with exact solutions, in order to compare my numerical solutions with it. I was able to find quite a few ...