Partially Penalized Immersed Finite Element Methods for Parabolic Interface Problems
Tao Lin, Qing Yang, Xu Zhang
TL;DR
This paper introduces partially penalized immersed finite element methods for efficiently solving parabolic interface problems on Cartesian grids, providing error estimates and numerical validation.
Contribution
It develops a novel partially penalized immersed finite element approach with theoretical error analysis for parabolic interface problems.
Findings
Error estimates in an energy norm are established.
Numerical examples confirm the theoretical results.
Abstract
We present partially penalized immersed finite element methods for solving parabolic interface problems on Cartesian meshes. Typical semi-discrete and fully discrete schemes are discussed. Error estimates in an energy norm are derived. Numerical examples are provided to support theoretical analysis.
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