On L²-error estimate for nonsymmetric interior penalty Galerkin approximation to linear elliptic problems with nonhomogeneous Dirichlet data

Abstract

In this paper, we present improved a priori error estimates for a nonsymmetric interior penalty Galerkin method (NIPG) with super-penalty for the problem -Δu = f in Ωand u = g on partial derivative Ω. Using piecewise polynomials of degree less than or equal to r, our new L(2)-error estimate is of order when g E H(r+1/2)(partial derivative Ω) and is optimal, i.e., of order (h/r)^(r+1) when g is an element of H^(r+1) (partial derivative Ω), where It denotes the mesh size. Numerical experiments are presented to illustrate the theoretical results.