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Results tagged with parabolic-pde
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user 549
A partial differential equation that describes diffusion phenomena.
2
votes
1
answer
148
views
Is it necessary to project the initial condition onto the variational space in a fully discr...
I'm solving a simple 1D heat diffusion problem $$u_t=u_{xx},\quad \Omega\times[0,T]$$ $$u=0\quad, \partial\Omega\times [0,T]$$ $$u(x,0)=f$$using a fully discrete galerkin finite element method. This …
- 12.2k
8
votes
1
answer
368
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
$$u(x,t …
- 12.2k