L2-NORM ERROR ANALYSIS OF THE HP-VERSION WITH NUMERICAL INTEGRATION

Title & Authors
L2-NORM ERROR ANALYSIS OF THE HP-VERSION WITH NUMERICAL INTEGRATION
Kim, Ik-Sung;

Abstract
We consider the hp-version to solve non-constant coefficient elliptic equations with Dirichlet boundary conditions on a bounded, convex polygonal domain $\small{\Omega}$ in $\small{R^{2}.}$ To compute the integrals in the variational formulation of the discrete problem we need the numerical quadrature rule scheme. In this paler we consider a family $\small{G_{p}= {I_{m}}}$ of numerical quadrature rules satisfying certain properties. When the numerical quadrature rules $\small{I_{m}{\in}G_{p}}$ are used for calculating the integrals in the stiffness matrix of the variational form we will give its variational fore and derive an error estimate of $\small{{\parallel}u-\tilde{u}^h_p{\parallel}_0,{\Omega}$
Keywords
the hp version;numerical quadrature rules;non-constant coefficients elliptic equation;
Language
English
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