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MiS Preprint

Boundary concentrated finite element methods

Boris N. Khoromskij and Jens Markus Melenk


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.

MSC Codes:
65N35, 65F10, 35D10
hp-finite element methods, preconditioning, data-sparse approximation to poincaré-steklov oper, meshes refined toward boundary

Related publications

2003 Repository Open Access
Boris N. Khoromskij and Jens Markus Melenk

Boundary concentrated finite element methods

In: SIAM journal on numerical analysis, 41 (2003) 1, pp. 1-36