Abstract
We study direct estimates for adaptive time-stepping finite element methods for time-dependent partial differential equations. Our results generalize previous findings from “On approximation classes for adaptive time-stepping finite element methods” by Actis et al. (2023), where the approximation error was only measured in L2([0,T],L2(Ω)). In particular, we now also cover the error norms L∞([0,T],L2(Ω)) and L2([0,T],H1(Ω)) which are more natural in this context.
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