Title: | Analysis of the FEM and DGM for an elliptic problem with a nonlinear Newton boundary condition (English) |

Author: | Feistauer, Miloslav |

Author: | Bartoš, Ondřej |

Author: | Roskovec, Filip |

Author: | Sändig, Anna-Margarete |

Language: | English |

Journal: | Proceedings of Equadiff 14 |

Volume: | Conference on Differential Equations and Their Applications, Bratislava, July 24-28, 2017 |

Issue: | 2017 |

Year: | |

Pages: | 127-136 |

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Category: | math |

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Summary: | The paper is concerned with the numerical analysis of an elliptic equation in a polygon with a nonlinear Newton boundary condition, discretized by the finite element or discontinuous Galerkin methods. Using the monotone operator theory, it is possible to prove the existence and uniqueness of the exact weak solution and the approximate solution. The main attention is paid to the study of error estimates. To this end, the regularity of the weak solution is investigated and it is shown that due to the boundary corner points, the solution looses regularity in a vicinity of these points. It comes out that the error estimation depends essentially on the opening angle of the corner points and on the parameter defining the nonlinear behaviour of the Newton boundary condition. Theoretical results are compared with numerical experiments confirming a nonstandard behaviour of error estimates. (English) |

Keyword: | Elliptic equation, nonlinear Newton boundary condition, monotone operator method, finite element method, discontinuous Galerkin method, regularity and singular behaviour of the solution, error estimation |

MSC: | 65N15 |

MSC: | 65N30 |

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Date available: | 2019-09-27T07:47:26Z |

Last updated: | 2019-09-27 |

Stable URL: | http://hdl.handle.net/10338.dmlcz/703041 |

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