SIAM Journal on Scientific Computing
A framework for intrinsic image processing on surfaces
Computer Vision and Image Understanding
A Convergent Finite Volume Scheme for Diffusion on Evolving Surfaces
SIAM Journal on Numerical Analysis
Journal of Computational Physics
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The aim of this paper is to investigate finite element methods for the solution of elliptic partial differential equations on implicitly defined surfaces. The problem of solving such equations without triangulating surfaces is of increasing importance in various applications, and their discretization has recently been investigated in the framework of finite difference methods. For the two most frequently used implicit representations of surfaces, namely level set methods and phase-field methods, we discuss the construction of finite element schemes, the solution of the arising discretized problems, and provide error estimates. The convergence properties of the finite element methods are illustrated by computations for several test problems.