Boundary concentrated finite element methods

Boris N. Khoromskij and Jens Markus Melenk

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Submission date: 18. Jul. 2001
Pages: 43
published in: SIAM journal on numerical analysis, 41 (2003) 1, p. 1-36 
DOI number (of the published article): 10.1137/S0036142901391852
Bibtex
MSC-Numbers: 65N35, 65F10, 35D10
Keywords and phrases: hp-finite element methods, preconditioning, data-sparse approximation to poincaré-steklov oper, meshes refined toward boundary
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Abstract:
A method with optimal (up to logarithmic terms) complexity for solving elliptic problems is proposed. The method relies on interior regularity but the solution may have globally low regularity due to rough boundary data or geometries. Elliptic regularity results, high order approximation results, and an efficient preconditioner are presented.

The method is utilized to realize, with linear-logarithmic complexity, an accurate and data-sparse approximations to the associated elliptic Poincaré-Steklov operators. Further applications include the treatment of exterior boundary value problems and its use in the framework of domain decomposition methods.