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Journal of Scientific Computing

Erschienen in:

05.11.2017

A Multi-Level Mixed Element Method for the Eigenvalue Problem of Biharmonic Equation

verfasst von: Shuo Zhang, Yingxia Xi, Xia Ji

Erschienen in: Journal of Scientific Computing | Ausgabe 3/2018

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Abstract

In this paper, we discuss approximating the eigenvalue problem of biharmonic equation. We first present an equivalent mixed formulation which admits natural nested discretization. Then, we present multi-level finite element schemes by implementing the algorithm as in Lin and Xie (Math Comput 84:71–88, 2015) to the nested discretizations on a series of nested grids. The multi-level mixed scheme for the biharmonic eigenvalue problem possesses optimal convergence rate and optimal computational cost. Both theoretical analysis and numerical verifications are presented.

Vorheriger Artikel Interior Penalties for Summation-by-Parts Discretizations of Linear Second-Order Differential Equations

Nächster Artikel A Parallel Partition of Unity Scheme Based on Two-Grid Discretizations for the Navier–Stokes Problem

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In this paper, \(\lesssim \), \(\gtrsim \), and

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denote \(\leqslant \), \(\geqslant \), and \(=\) up to a constant respectively. The hidden constants depend on the domain, and, when triangulation is involved, they also depend on the shape-regularity of the triangulation, but they do not depend on h or any other mesh parameter.

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Titel: A Multi-Level Mixed Element Method for the Eigenvalue Problem of Biharmonic Equation
verfasst von: Shuo Zhang
Yingxia Xi
Xia Ji
Publikationsdatum: 05.11.2017
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 3/2018
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-017-0592-7

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