Analysis demonstrates optimal approximations for heat equation using finite element method, suggesting efficient local mesh refinements.
We present a space-time finite element method for the heat equation that computes quasi-optimal approximations with respect to natural norms while incorporating local mesh refinements in space-time. The discretized problem is solved with a conjugate gradient method with an (nearly) optimal preconditioner.
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Diening et al. (2025) studied this question.
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