Geodesic
The finite element solution of parabolic equations
Applications of Mathematics, Tome 23 (1978) no. 6, pp. 408-438.

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In contradistinction to former results, the error bounds introduced in this paper are given for fully discretized approximate soltuions of parabolic equations and for arbitrary curved domains. Simplicial isoparametric elements in $n$-dimensional space are applied. Degrees of accuracy of quadrature formulas are determined so that numerical integration does not worsen the optimal order of convergence in $L_2$-norm of the method.
DOI : 10.21136/AM.1978.103769
Classification : 35K60, 65N15, 65N30
Keywords: error bounds; approximate solutions; parabolic equations; arbitrary curved domains; quadrature formulas; optimal order of convergence 
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Nedoma, Josef. The finite element solution of parabolic equations. Applications of Mathematics, Tome 23 (1978) no. 6, pp. 408-438. doi : 10.21136/AM.1978.103769. http://geodesic.mathdoc.fr/articles/10.21136/AM.1978.103769/

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