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Keywords:
error bounds; approximate solutions; parabolic equations; arbitrary curved domains; quadrature formulas; optimal order of convergence
error bounds; approximate solutions; parabolic equations; arbitrary curved domains; quadrature formulas; optimal order of convergence
Summary:
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.
References:
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