| Abstract: |
| Finite element exterior calculus provides a unified framework for analyzing the stability and convergence of mixed finite element discretizations of partial differential equations. Structure preservation plays a key role in this analysis, since it relies on the use of finite element spaces that form a subcomplex of the de Rham complex. The framework was originally developed for elliptic PDEs on open domains in Euclidean space, but recent efforts have extended it to time-dependent PDEs and PDEs on static surfaces. We extend the framework to another setting: parabolic PDEs posed on surfaces that evolve with time in a prescribed fashion. We prove a priori error estimates for numerical discretizations of such problems, taking into account variational crimes (discrepancies between the geometry of the exact and approximate surfaces) in the analysis. |
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