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