### 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.

Original language | German |
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Pages (from-to) | 253-265 |

Number of pages | 13 |

Journal | Computing |

Volume | 13 |

Issue number | 3-4 |

DOIs | |

State | Published - Sep 1974 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Computational Theory and Mathematics

### Cite this

**Die Approximation der Lösungen gemischter Randwertprobleme quasilinearer elliptischer Differentialgleichungen.** / Mittelmann, Hans.

Research output: Contribution to journal › Article

*Computing*, vol. 13, no. 3-4, pp. 253-265. https://doi.org/10.1007/BF02241719

}

TY - JOUR

T1 - Die Approximation der Lösungen gemischter Randwertprobleme quasilinearer elliptischer Differentialgleichungen

AU - Mittelmann, Hans

PY - 1974/9

Y1 - 1974/9

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=0016360123&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0016360123&partnerID=8YFLogxK

U2 - 10.1007/BF02241719

DO - 10.1007/BF02241719

M3 - Article

VL - 13

SP - 253

EP - 265

JO - Computing

JF - Computing

SN - 0010-485X

IS - 3-4

ER -