Parabolic2D

Solves the 2D heat equation with Dirichlet boundary conditiions

\[u_t = - \nu \nabla^2 u\]

with $x \in [0, 2]$ and $y \in [0, 2]$.

The boundary conditions are given by

\[a u + b \nabla u \cdot \hat n = g\]

with $a = 1$, $b = 0$, and $g = 0$, which is equivalent to Dirichlet conditions along each boundary. This corresponds to the call to addScalarBC! of addScalarBC!(A, b, k, m, dx, n, dy, bc), where A is the operator matrix, b is the right hand side vector, and bc is a boundary condition sturc that contains the tuples dc, nc, and v which hold the coefficients for $a$, $b$, and $g$ in the above systems of equations. dc $= (1.0, 1.0, 1.0, 1.0)$, nc $= (0.0, 0.0, 0.0, 0.0)$, and v is composed of 4 vectors which all contain $0.0$.

There is no analytical solution.

This examples is implemented in parabolic2D.jl