Estimates of discrete time derivatives for the parabolic-parabolic Robin-Robin coupling method
arxiv(2024)
摘要
We consider a loosely coupled, non-iterative Robin-Robin coupling method
proposed and analyzed in [J. Numer. Math., 31(1):59–77, 2023] for a
parabolic-parabolic interface problem and prove estimates for the discrete time
derivatives of the scalar field in different norms. When the interface is flat
and perpendicular to two of the edges of the domain we prove error estimates in
the H^2-norm. Such estimates are key ingredients to analyze a defect
correction method for the parabolic-parabolic interface problem. Numerical
results are shown to support our findings.
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