FEniCS Course - FEniCS Project

FEniCS programming exercise: heat equationConsider the heat equation problem:with∂u∂t − ∆u = f in Ω = [0, 1]2 for t > 0u(x, t) = g(x, t) for x ∈ ∂Ω for t > 0u(x, 0) = g(x, 0) for x ∈ Ωf = β − 2 − 2αg(x, t) = 1 + x 2 0 + αx 2 1 + βt (x = (x 0 , x 1 ))Ex. 1 Compute an approximated solution at T = 1.8Ex. 2 Compare the approximated solution to the exact solutionat T = 1.8. How large is the error (in the eyenorm and inthe L 2 (Ω) norm)?Ex. 3 Compute an approximated solution with the same set-upbut on Ω = [0, 1] 3 ⊂ R 3 .13 / 13