Improved a priori error estimates for a space-time finite element method for parabolic problems
Abstract
In this paper, we employ a space-time finite element method to discretize the parabolic initial-boundary value problem and extend its error analysis with refined estimates on unstructured space-time meshes. We establish higher-order estimates in three different norms, thereby supplementing existing research. Moreover, we obtain an optimal estimate in a norm stronger than that of the trial space. Finally, we present numerical examples to illustrate our theoretical results.
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