A finite element method on composite grids based on Nitsche's method

Anita Hansbo (1) , Peter Hansbo (2) , Mats G. Larson (3)

1 Department of Informatics and Mathematics
2 Department of Applied Mechanics
3 Department of Mathematics

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.

Mots clés: Nitsche’s method; overlapping grids

Domaines: Sciences de l'ingénieur [physics]

Anita Hansbo, Peter Hansbo, Mats G. Larson. A finite element method on composite grids based on Nitsche's method. ESAIM: Mathematical Modelling and Numerical Analysis, 2003, 37 (3), pp.495-514. ⟨10.1051/m2an:2003039⟩. ⟨hal-01353508⟩