Optimal a priori estimates for higher order finite elements for elliptic interface problems
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AbstractWe analyze higher order finite elements applied to second order elliptic interface problems. Our a priori error estimates in the L(2)- and H(1)-norm are expressed in terms of the approximation order p and delta parameter A that quantifies how well the interface is resolved by the finite element mesh. The optimal p-th order convergence in the H(1)(Omega)-norm is only achieved under stringent assumptions on delta, namely, delta = O(h(2p)). Under weaker conditions on delta, optimal a priori estimates can be established in the L(2-) and in the H(1) (Omega(delta))-norm, where Omega(delta) is a subdomain that excludes a tubular neighborhood of the interface of width O(delta). In particular, if the interface is approximated by an interpolation spline of order p and if full regularity is assumed, then optimal convergence orders p + 1 and p for the approximation in the L(2)(Omega)- and the H(1) (Omega(delta))-norm can be expected but not order p for the approximation in the H(1)(Omega)-norm. Numerical examples in 2D and 3D illustrate and confirm our theoretical results. (C) 2009 IMACS. Published by Elsevier B.V. All rights reserved.
All Author(s) ListLi JZ, Melenk JM, Wohlmuth B, Zou J
Journal nameApplied Numerical Mathematics
Volume Number60
Issue Number1-2
Pages19 - 37
LanguagesEnglish-United Kingdom
KeywordsA priori estimates; Elliptic interface problems; Higher order finite elements; Optimal convergence rates
Web of Science Subject CategoriesMathematics; Mathematics, Applied; MATHEMATICS, APPLIED

Last updated on 2021-20-09 at 23:39