An Adaptive Strategy for the Local Discontinuous Galerkin Method Applied to Porous Media Problems

Abstract

Abstract: We present a numerical study of an adaptive technique for solving steady fluid flow problems through porous media in 2D using a discontinuous Galerkin (DG) method, the so‐called Local Discontinuous Galerkin (LDG) method. DG methods may be viewed as high‐order extensions of the classical finite volume method and, since no interelement continuity is imposed, they can be defined on very general meshes, including nonconforming meshes, making these methods suitable for h‐adaptivity. The technique starts with an initial conformal spatial discretization of the domain and, in each step, the error of the solution is estimated. The mesh is locally modified according to the error estimate by performing two local operations: refinement and agglomeration. This procedure is repeated until the solution reaches a desired accuracy. The performance of this technique is examined through several numerical experiments and results are compared with globally refined meshes in examples with known analytic solutions.