L_2-norm error analysis of the HP-version with numerical integration

Abstract

We consider the hp-version to solve non-constant coefficientselliptic equations with Dirichlet boundary conditions on a bounded,convex polygonal domain Omega in R^2. To compute the integralsin the variational formulation of the discrete problem we need thenumerical quadrature rule scheme. In this paper we consider a familyG_p ={ I_m } of numerical quadrature rules satisfying certainproperties. When the numerical quadrature rules I_m in G_pare used for calculating the integrals in the stiffness matrixof the variational form we will give its variational form andderive an error estimate of {|u-widetilde u_p^h |}_{0,Omega}.