대한수학회논문집 (Communications of the Korean Mathematical Society)
- 제11권2호
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- Pages.503-514
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- 1996
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- 1225-1763(pISSN)
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- 2234-3024(eISSN)
On the $L_2(\Omega)$ -error for the p-version under numerical quadrature rules
초록
We consider non-constant coefficient elliptic equations of the type -div(a \bigtriangledown u) = f$, and employ the P-version of the finite element method as a numerical method for the approximate solutions. To compute the integrals in the variational form of the discrete problem we need the numerical quadrature rule scheme. In practice the integrations are seldom computed exactly. In this paper, we give an $L_2(\Omega)$-error estimate of $\Vert u = \tilde{u}_p \Vert_{0,omega}$ in comparison with $\Vert u = \tilde{u}_p \Vert_{1,omega}$, under numerical quadrature rules which are used for calculating the integrations in each of the stiffness matrix and the load vector.
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