All Questions
Tagged with pde finite-element
160
questions
1
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1
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61
views
How to constraint the tangential gradient on a boundary in FEniCS?
The problem I'm considering is a 2D scalar PDE.
The domain $\Omega$ is a disk with two holes $\partial\Omega_1$ and $\partial\Omega_2$ and an external boundary $\partial\Omega_0$.
The PDE and boundary ...
1
vote
1
answer
127
views
How to refine $h$ and $\Delta t$ for convergence tests on evolution PDE
Setting
I am solving for $u(x,y,t)$ the wave equation $\partial_{tt} u - \partial_{xx} u = f$ on $(x,y)\in\Omega=[0,1]\times \mathbb{R}$ by splitting it into an equivalent first order system:
$$\...
- 13
1
vote
0
answers
84
views
Seeking open-source PDE Solver for inhomogeneous material properties
I'm currently in search of an open-source PDE solver (Finite Element Method is preferred) that can effectively handle the challenge of material properties coefficients associated with each element in ...
- 11
0
votes
0
answers
64
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How to set Neumann BC for coupled transport problem in weak form?
Consider
$$\begin{aligned}
\partial_t v + b\cdot \nabla \phi &=0 \\
\partial_t \phi + b\cdot \nabla v &= 0
\end{aligned}$$
for $v:(x,y)\mapsto \mathbb{R}$, unknown and time-dependent ($...
3
votes
2
answers
279
views
Solving systems of advection-diffusion-reaction equations with finite element methods
I have been doing a lot of self-study on numerically solving PDEs so that I can solve system of linear and nonlinear Advection-Diffusion-Reaction (ADR) systems on complex meshes.
I have been watching ...
- 297
0
votes
0
answers
53
views
PETSC: Solving a simpler PDE results in error while solving the original equation works in snes/tutorials/ex13.c
In snes/tutorials/ex13.c,
there is a function SetupPrimalProblem(),
which sets up the $f_0$ and $f_1$ in ...
- 101
0
votes
0
answers
81
views
How to get damping matrix for structural model in FE analysis
I need to implement in C a method of obtaining transient solution of damped FE models based on modal results for a structural model (imported CAD geometry) defined with hysteretic (structural) damping....
- 1
5
votes
2
answers
339
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Continuous vs discontinuous space-time FEM
What are some reasons for approximating a (e.g. parabolic) PDE using the space-time method, with continuous finite elements in time, vs discontinuous finite elements in time?
Are there e.g. ...
- 259
2
votes
2
answers
260
views
Errors imposing boundary conditions weakly with DG
I am using interior penalty discontinuous Galerkin to solve a simple Laplace problem:
\begin{align*}
\nabla u=0
\end{align*}
with prescribed 0 and 1 Dirichlet boundary conditions on opposite edges of ...
- 506
2
votes
1
answer
796
views
Meaning of Degree of Freedom in FEM
Assume we want to solve the Poisson eq. with the FEM on some Domain $\Omega$, i.e.
$$\begin{cases} -\Delta u = f, \; \Omega\\
u = 0, \; \partial \Omega \end{cases}$$
For the sake of the discussion let ...
- 123
1
vote
0
answers
189
views
Solving second order coupled differential equations in python
as I have to design a reactor and therefore have to get its length x, I have to solve the following differential equations:
$$D_{eg}\tfrac{d^2A_g}{dx^2}-u_g\tfrac{dA_g}{dx} = k_la_b\left(\tfrac{A_g}{...
- 11
4
votes
0
answers
241
views
Spurious oscillations in solving diffusion problems using finite elements
I've been struggling with this problem for a while so I hope someone can help me here.
I'm trying to solve the McNabb-Foster equations for hydrogen diffusion in metals using a simple 1D finite element ...
- 41
1
vote
1
answer
143
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 ...
user43841
1
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0
answers
102
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Numerical methods for $u_t+c u_x= \frac{-c}{x}u$?
I am looking for possible numerical methods to solve the PDE
$$u_t+c u_x= \frac{-c}{x}u$$
I am particularly interested in a Finite elements method, although I am also curious if you can expose some ...
- 151
1
vote
1
answer
124
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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 ...
- 21