A finite element method on composite grids based on Nitsche's method
Department of Informatics and Mathematics, University of Trollhättan Uddevalla, Box 957, 461 39 Trollhättan, Sweden. firstname.lastname@example.org.
2 Department of Applied Mechanics, Chalmers University of Technology, 412 96 Göteborg, Sweden.
3 Department of Mathematics, Chalmers University of Technology, 412 96 Göteborg, Sweden.
Revised: 6 March 2003
In this paper we propose a finite element method for the approximation of second order elliptic problems on composite grids. The method is based on continuous piecewise polynomial approximation on each grid and weak enforcement of the proper continuity at an artificial interface defined by edges (or faces) of one the grids. We prove optimal order a priori and energy type a posteriori error estimates in 2 and 3 space dimensions, and present some numerical examples.
Mathematics Subject Classification: 65N12 / 65N30
Key words: Nitsche's method / overlapping grids.
© EDP Sciences, SMAI, 2003