An Intrinsically Parallel Finite Element Method

We show that the weakly over-penalized symmetric interior penalty (WOPSIP) method has high intrinsic parallelism. Consider the following model problem: Find u ∈ H 0 (Ω) such that a(u, v) = ∫ Ω fv dx ∀ v ∈ H 0 (Ω), where Ω ⊂ R is a bounded polygonal domain, f ∈ L2(Ω), and a(w, v) = ∫ Ω ∇w · ∇v dx. This problem can be solved by the weakly over-penalized symmetric interior penalty (WOPSIP) method [4, 3, 2] as follows. Let Th be a simplicial triangulation of Ω and Vh be the corresponding discontinuous P1 finite element space, i.e., Vh = {v ∈ L2(Ω) : vT = v ∣