Residual-based

In this article, we develop the a posteriori error analysis of a space-time discontinuous Galerkin finite element method for the Richards equation. Computable upper and lower bounds on the error in a residual dual norm are derived, which are explicit in the mesh size. Several numerical experiments demonstrate the performance of the a posteriori error bound within an mesh refinement algorithm, which refines the mesh as time evolves. Although this a posteriori error bound is on the residual dual norm, and is not a upper bound for the H1-norm, it is able to refine the areas of the mesh where the residual is large in a manner which reduces the H1-error and L1-error as well.