Finite Elements for the Beltrami operator on arbitrary surfaces

  • Gerhard Dziuk
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 1357)

Abstract

We develop a Finite Element Method for elliptic differential equations on arbitrary two-dimensional surfaces. Global para metrizations are avoided. We prove asymptotic error estimates. Numerical examples are calculated.

Keywords

Finite Elements Beltrami Operator Elliptic Equations on Surfaces Classification Numbers 65 N 30 35 A 40 

References

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    Ciarlet, P.G.: The Finite Element Method for Elliptic Problems. (1987) Amsterdam-New York-OxfordGoogle Scholar
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    Nedelec, J.C.: Curved Finite Element Methods for the Solution of Integral Singular Equations on Surfaces in ℝ3. Computing Methods in Appl. Sciences and Engeneering (1976), 374–390, Lecture Notes in Economics and Math. SystemsGoogle Scholar
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    Steger, L.K.: Sphärische Finite Elemente und ihre Anwendung auf Eigenwertprobleme des Laplace-Beltrami-Operators. Dissertation München (1983)Google Scholar
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    Wloka, J.: Partielle Differentialgleichungen. Stuttgart (1982)Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Gerhard Dziuk
    • 1
  1. 1.Institut für Angewandte MathematikBonnFRG

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