Abstract
We consider mixed boundary value problems for elliptic differential equations of second order in the plane that are the Euler-equations of a variational problem. The boundary conditions include Dirichlet’s problem and the third boundary value problem. As trial functions for the finite element method we use piecewise polynomials of arbitrary degree, which can be either Lagrange — or Hermite — interpolation polynomials. Generalizing known results stability theorems are given including the case of isoparametric elements. A minimal and a capillary surface are computed using quadratic isoparametric elements.
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Mittelmann, H.D. (1975). Stabilität bei der Methode der Finiten Elemente for Quasilineare Elliptische Randwertprobleme. In: Numerische Behandlung von Differentialgleichungen. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 27. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5532-7_13
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DOI: https://doi.org/10.1007/978-3-0348-5532-7_13
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