A staggered DG method of minimal dimension for the Stokes equations on general meshes

Abstract

In this paper, a locally conservative, lowest order staggered discontinuous Galerkin method is developed for the Stokes equations. The proposed method allows rough grids and is based on the partition of the domain into arbitrary shapes of quadrilaterals or polygons, which makes the method highly desirable for practical applications. A priori error analysis covering low regularity is demonstrated. A new postprocessing scheme for the velocity earning faster convergence is constructed. Next, adaptive mesh refinement is highly appreciated on quadrilateral and polygonal meshes since hanging nodes are allowed. Therefore, we propose two guaranteed-type error estimators in L2 error of stress and energy error of the postprocessed velocity, respectively. Numerical experiments confirm our theoretical findings and illustrate the flexibility of the proposed method and accuracy of the guaranteed upper bounds.