Improving the rate of convergence of 'high order finite elements' on polygons and domains with cusps

Abstract

Let u and uV ∈ V be the solution and, respectively, the discrete solution of the non-homogeneous Dirichlet problem u = f onP, u|∂P = 0. For any m ∈ N and any bounded polygonal domain P, we provide a construction of a new sequence of finite dimensional subspaces Vn such that ‖u− uVn‖H 1 ≤ C dim(Vn)−m/2‖f ‖Hm−1 , where f ∈ Hm−1(P) is arbitrary and C is a… (More)
DOI: 10.1007/s00211-005-0588-3

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