Penalty algorithm adapted for the spectral element discretization of the Darcy equations

Abstract

Abstract Any spectral element discretization of the Darcy problem can be efficiently solved by applying the penalty method. This method leads to a system of equations with uncoupled unknowns. We prove a posteriori error estimates for a spectral element discretization of the Darcy problem. The proposed algorithm permits the optimization of the penalty parameter as a function of the error indicators.

Keywords

• Penalty method
• Darcy equations
• Spectral element discretization