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

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 Ω and u=g on ∂Ω. Using piecewise polynomials of degree less than or equal to r, our new L2-error estimate is of order (h/r)r+1/2 when g∈Hr+1/2(∂Ω) and is optimal, i.e., of order (h/r)r+1 when g∈Hr+1(∂Ω), where h denotes the mesh size. Numerical experiments are presented to illustrate the theoretical results.