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Numerical Algorithms

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25.06.2019 | Original Paper

High-precision computation of the weak Galerkin methods for the fourth-order problem

verfasst von: John Burkardt, Max Gunzburger, Wenju Zhao

Erschienen in: Numerical Algorithms | Ausgabe 1/2020

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Abstract

The weak Galerkin form of the finite element method, requiring only C⁰ basis function, is applied to the biharmonic equation. The computational procedure is thoroughly considered. Local orthogonal bases on triangulations are constructed using various sets of interpolation points with the Gram-Schmidt or Levenberg-Marquardt methods. Comparison and high-precision computations are carried out, and convergence rates are provided up to degree 11 for L², 10 for H¹, and 9 for H², suggesting that the algorithm is useful for a variety of computations.

Vorheriger Artikel Unfitted finite element for optimal control problem of the temperature in composite media with contact resistance

Nächster Artikel Approximation properties and error estimation of q-Bernstein shifted operators

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Titel: High-precision computation of the weak Galerkin methods for the fourth-order problem
verfasst von: John Burkardt
Max Gunzburger
Wenju Zhao
Publikationsdatum: 25.06.2019
Verlag: Springer US
Erschienen in: Numerical Algorithms / Ausgabe 1/2020
Print ISSN: 1017-1398
Elektronische ISSN: 1572-9265
DOI: https://doi.org/10.1007/s11075-019-00751-5

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