An adaptive finite element method for the Laplace-Beltrami operator on implicitly defined surfaces

摘要

We present an adaptive finite element method for approximating solutions to the Laplace-Beltrami equation on surfaces in 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.