Error estimate for a finite element approximation of the solution of a linear parabolic equation on a two-dimensional surface
arXiv:1604.046652 citationsh-index: 2
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This is an incremental theoretical extension for researchers working on finite element methods for surface PDEs.
The paper extends an existing error estimate for finite element approximations of the heat equation on a 2D Euclidean domain to a general linear parabolic equation on a 2D surface, proving the estimate holds in this broader context.
We show that a certain error estimate for a fully discrete finite element approximation of the solution of the heat equation which is defined in a two-dimensional Euclidean domain carries over to the case of a general linear parabolic equation which is defined on a two-dimensional surface.