Low Regularity Error Analysis for Weak Galerkin Finite Element Methods for Second Order Elliptic Problems

This paper presents error estimates in both an energy norm and the $L^2$-norm for the weak Galerkin (WG) finite element methods for elliptic problems withlow regularity solutions. The error analysis for the continuous Galerkin finite element remains same regardless of regularity. A totally different analysis is needed fordiscontinuous finite element methods if the elliptic regularity is lower than H-1.5.Numerical results confirm the theoretical analysis.