A Posteriori Error Analysis of Penalty Domain Decomposition Methods for Linear Elliptic Problems

Abstract

In this work we introduce a new version of the non-overlapping domain decomposition method (DDM) method proposed by Chacon and Chacon in [5]. In the new method a H 00 1/2 (Γ) penalty term replaces the L2(Γ) one in the original method. We develop a posteriori error analysis, aimed to design strategies for optimizing the combined choice of the penalty parameter and the adaptation of the grid, to reduce the computational cost. We shall discuss the computational benefits of using H 00 1/2 (Γ) penalty versus L2(Γ) penalty.