Computing and Visualization in Science

, Volume 12, Issue 3, pp 87–100 | Cite as

Finite element approximation of elliptic partial differential equations on implicit surfaces

  • Martin BurgerEmail author
Regular article


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.


Weak Solution Implicit Representation Finite Element Approximation Elliptic Partial Differential Equation Implicit Surface 
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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Institut für Numerik und Angewandte MathematikWestfälische Wilhelms-Universität MünsterMünsterGermany

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