Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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ERROR ANALYSIS OF THE hp-VERSION UNDER NUMERICAL INTEGRATIONS FOR NON-CONSTANT COEFFICIENTS

  • KIM, IK-SUNG (Department of Applied Mathematics Korea Maritime University)
  • Received : 2005.05.03
  • Published : 2005.06.25
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Abstract

In this paper we consider the hp-version to solve non-constant coefficients elliptic equations on a bounded, convex polygonal domain ${\Omega}$ in $R^2$. A family $G_p=\{I_m\}$ of numerical quadrature rules satisfying certain properties can be used for calculating the integrals. When the numerical quadrature rules $I_m{\in}G_p$ are used for computing the integrals in the stiffness matrix of the variational form we will give its variational form and derive an error estimate of ${\parallel}u-{\widetilde{u}}^h_p{\parallel}_{1,{\Omega}$.

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References

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