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.
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

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