An Adaptive Finite Element Method for the Laplace-Beltrami Operator on Implicitly Defined Surfaces

Authors:
Alan Demlow;Gerhard Dziuk
Affiliations:
-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2007

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Abstract

We present an adaptive finite element method for approximating solutions to the Laplace-Beltrami equation on surfaces in $\mathbb{R}^3$ which may be implicitly represented as level sets of smooth functions. Residual-type a posteriori error bounds which show that the error may be split into a “residual part” and a “geometric part” are established. In addition, implementation issues are discussed and several computational examples are given.