5 research outputs found
Discontinuous Galerkin Methods for Second-Order Elliptic PDE with Low-Regularity Solutions
In this paper we derive an a priori error analysis for interior penalty discontinuous Galerkin finite element discretizations of the Poisson equation with exact solution inW 2,p , p∈(1,2]. We show that the DGFEM converges at an optimal algebraic rate with respect to the number of degrees of freedo
A Computational Study of the Weak Galerkin Method for Second-Order Elliptic Equations
The weak Galerkin finite element method is a novel numerical method that was
first proposed and analyzed by Wang and Ye for general second order elliptic
problems on triangular meshes. The goal of this paper is to conduct a
computational investigation for the weak Galerkin method for various model
problems with more general finite element partitions. The numerical results
confirm the theory established by Wang and Ye. The results also indicate that
the weak Galerkin method is efficient, robust, and reliable in scientific
computing.Comment: 19 page
Error analysis of discontinuous Galerkin methods for Stokes problem under minimal regularity
In this article, we analyze several discontinuous Galerkin methods (DG) for the
Stokes problem under the minimal regularity on the solution. We assume that the velocity
u belongs to [H1 0 ()]d and the pressure p 2 L2 0 (). First, we analyze standard DG methods assuming that the right hand side f belongs to [H¡1() \ L1()]d. A DG method that is well de¯ned for f belonging to [H¡1()]d is then investigated. The methods under study
include stabilized DG methods using equal order spaces and inf-sup stable ones where the pressure space is one polynomial degree less than the velocity space.Preprin