A Posteriori Error Estimate and Mesh Adaptation for the Numerical Solution of the Richards Equation

Abstract

We solve the Richards equation, describing porous media flows, by the space-time discontinuous Galerkin method. We derive a posteriori error estimates using the spatial and temporal reconstructions and obtain an upper bound of the error measured in the dual norm with any unknown constant.

We present a numerical example demonstrating the use of the error estimators for a practical problem.

Keywords

• A posteriori error estimate
• Mesh adaptation
• Richards equation