Die Approximation der Lösungen gemischter Randwertprobleme quasilinearer elliptischer Differentialgleichungen

H. D. Mittelmann

doi:10.1007/BF02241719

Die Approximation der Lösungen gemischter Randwertprobleme quasilinearer elliptischer Differentialgleichungen

Translated title of the contribution: The approximate solution of mixed boundary-value problems for quasilinear elliptic differential equations

H. D. Mittelmann

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We consider boundary-value problems for differential equations, which are the Euler-Lagrange-equation of a variational problem that contains an additional integral along the boundary of the plane domain. For a discrete analogue of the variational problem we prove the existence of a unique solution and the discrete convergence of this solution to the solution of the continuous problem if the width of the mesh is refined. The shape of a capillary surface is computed using the given discretization and the SOR-Newton-algorithm.

Translated title of the contribution	The approximate solution of mixed boundary-value problems for quasilinear elliptic differential equations
Original language	German
Pages (from-to)	253-265
Number of pages	13
Journal	Computing
Volume	13
Issue number	3-4
DOIs	https://doi.org/10.1007/BF02241719
State	Published - Sep 1974
Externally published	Yes

ASJC Scopus subject areas

Software
Theoretical Computer Science
Numerical Analysis
Computer Science Applications
Computational Theory and Mathematics
Computational Mathematics

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10.1007/BF02241719

Cite this

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abstract = "We consider boundary-value problems for differential equations, which are the Euler-Lagrange-equation of a variational problem that contains an additional integral along the boundary of the plane domain. For a discrete analogue of the variational problem we prove the existence of a unique solution and the discrete convergence of this solution to the solution of the continuous problem if the width of the mesh is refined. The shape of a capillary surface is computed using the given discretization and the SOR-Newton-algorithm.",

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AB - We consider boundary-value problems for differential equations, which are the Euler-Lagrange-equation of a variational problem that contains an additional integral along the boundary of the plane domain. For a discrete analogue of the variational problem we prove the existence of a unique solution and the discrete convergence of this solution to the solution of the continuous problem if the width of the mesh is refined. The shape of a capillary surface is computed using the given discretization and the SOR-Newton-algorithm.

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Die Approximation der Lösungen gemischter Randwertprobleme quasilinearer elliptischer Differentialgleichungen

Abstract

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