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MiS Preprint

An efficient direct solver for the boundary concentrated FEM in 2D

Boris N. Khoromskij and Jens Markus Melenk


The boundary concentrated FEM, a variant of the hp-version of the finite element method, is proposed for the numerical treatment of elliptic boundary value problems. It is particularly suited for equations with smooth coefficients and boundary conditions that may have low Sobolev regularity. In the two-dimensional case, it is shown that the Cholesky factorization of the resulting stiffness matrix requires O( N log4N) units of storage and can be computed with O( N log8N) work. Numerical results confirm theoretical estimates.

MSC Codes:
65N35, 65F10, 35D10
hp-finite element methods, meshes refined towards boundary, direct solvers, schur complement

Related publications

2002 Repository Open Access
Jens Markus Melenk and Boris N. Khoromskij

An efficient direct solver for the boundary concentrated FEM in 2D

In: Computing, 69 (2002) 2, pp. 91-117