We consider a second order elliptic boundary value problem in the variational form: find u~* ∈ H_0~1(Ω), for a given polygonal (polyhedral) domain Ω is contained in R~d, d = 2,3 and a source term f ∈ L~2(Ω), such that ≡a(u~*,v){(∫_Ω ▽u~*(x) ? ▽v(x) dx) = ≡(f,v){( ∫_Ω f(x)v(x) dx), for all v ∈ H_0~1(Ω). (1) The Bank-Hoist parallel adaptive meshing paradigm is utilised to solve (1) in a combination of domain decomposition and adaptivity. It can be summarised as follows: Step Ⅰ-Mesh Partition: Starting with a coarse mesh Th, the domain is partitioned into non-overlapping subdomains: Ω = ∪_(i=1)~p Ω_i.
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