All Questions
Tagged with pde parabolic-pde
52
questions
0
votes
0
answers
56
views
What is the best finite volume method for the following equation?
I'm trying to create a partial differential equation that approximates 1-D climate in a rocky planet's atmosphere, which accounts for energy transport via radiation and convection. I am only ...
- 317
0
votes
1
answer
56
views
Time discretisation after splitting a 4th order equation
Suppose we have a fourth-order parabolic PDE
$$\partial_t u + a(t)\Delta( \Delta u) - div( b(x,t)\nabla u) =0$$
We split the equation into two second-order equations by introducing $w = \Delta u$ thus
...
- 3
3
votes
0
answers
158
views
Form of nonlinear diffusion equation
Consider the following nonlinear diffusion problem,
$$
\frac{\partial u}{\partial t} = x^{-2}\frac{\partial}{\partial x}\left(x^2 u^4 \frac{\partial u}{\partial x}\right), \quad 0 < x < 1
$$
We ...
- 617
0
votes
1
answer
175
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How do I use pdepe for a first order parabolic PDE with only one boundary condition?
I am trying to use Matlab's pdepe.m to solve the first order parabolic PDE
$$\frac{\partial u}{\partial x}+\frac{\partial u}{\partial x}=x$$
I have not had trouble coding the argument of pdepe @pdefun:...
5
votes
2
answers
339
views
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
0
answers
88
views
Numerical scheme for the heat equation on the icosahedral hexagonal grid
I have a predefined grid(like this) that is spawned from a regular icosahedradron. It consists of many hexagons and 12 pentagons (corresponding to icosahedradron vertexes). I can tweak the granularity ...
- 121
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
1
answer
164
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Non-Linear advection diffusion with nondifferetiable advection term
I'm looking at Murray's book: Mathematical biology: an introduction , first volume, pag. 404
In particular, I'm interested to solve the following PDE:
$$\partial_t u = \partial_x (\text{sign}(x) u) + \...
- 309
0
votes
0
answers
87
views
fixed point iteration on DD method
I have to solve the the problem $u_t+\Delta^2u=f(u)$, where $f(u)$ is non-linear, using domain-decomposition method.
My approach is first using fixed point iteration on mixed form i.e to say $u^{k+1}...
- 41
3
votes
1
answer
187
views
Type of Rosenbrock method by its coefficients
A Fortran code that solves stiff PDE systems contains the following arrays of Rosenbrock-Wanner method coefficients:
...
- 226
1
vote
1
answer
212
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How suitable is multigrid method for time-dependent PDEs?
For elliptic PDEs (Poisson-type), the multigrid method is very sufficient, but how about time-dependent problems (i.e parabolic or hyperbolic PDEs)?
Is it efficient to solve such problems using a ...
- 481
0
votes
0
answers
74
views
Solving Parabolic PDE using Matlab
I have the following pde (Burger's equation)
for $\epsilon>0: u_t+u.u_x=\epsilon.u_{xx}$ and $x\in \mathbb{R},t>0$
and the initial condition: $u(x,0)=\phi(x)=1_{(-\infty,0)}(x)$.
I want ...
- 109
1
vote
0
answers
66
views
Discretizing a parabolic PDE with finite volume method
I want to discretize the following parabolic PDE:
$$u_t = \nabla\cdot(\alpha(x)\nabla u)- \beta u\\
x\in\Omega \subset \mathbb{R}^2\\
\partial_n u = 0\\
u(t,0) = u_0(x)\ge 0, \alpha(x)>0$$
Given ...
- 226
1
vote
1
answer
91
views
Physical data for heat equation
I want to implement an algorithm to solve a heat equation, i.e.
\begin{align*}
\partial_t u - \Delta u = f \text{ in } \Omega\times(0,T)\\
\partial_nu = 0 \text{ in } \partial\Omega \times (0,T)\\
u(0)...
- 13
0
votes
1
answer
121
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Parabolic differential equations with time delay
Let $d_1=1,d_2=2,a_{11}=\frac{5}{13},a_{12}=\frac{22}3,a_{21}=-2,a_{22}=\frac{6}7,\tau=\frac{5}7$, $\psi(t,x)=\cos^42x,\phi(t,x)=\frac{3}{13}x^4\sin^2 3x$, $\Omega=[0,200]$
How to solve:
$$\left\{
\...
- 729