We present an adaptive finite element method for approximating solutions to the Laplace–Beltrami equation on surfaces in R³ 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.
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Demlow et al. (2007) studied this question.
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