A FULLY DISCRETE PLATES COMPLEX ON POLYGONAL MESHES WITH APPLICATION TO THE KIRCHHOFF-LOVE PROBLEM

被引：7

作者：

Di Pietro, Daniele A. ^{[1
]}

Droniou, Jerome ^{[2
]}

机构：

[1] Univ Montpellier, IMAG, CNRS, Montpellier, France

[2] Monash Univ, Sch Math, Melbourne, Australia

来源：

MATHEMATICS OF COMPUTATION | 2023年 / 92卷 / 339期

关键词：

Discrete de Rham method; compatible discretisations; mixed formu-lation; plates complex; biharmonic equation; Kirchhoff-Love plates; HERRMANN-JOHNSON METHOD; FINITE-ELEMENT METHODS; MIXED METHODS; DECOMPOSITION RESULT; ELLIPTIC PROBLEMS; BENDING PROBLEMS; ARBITRARY-ORDER; DISCRETIZATION; DIFFUSION;

D O I：

10.1090/mcom/3765

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work we develop a novel fully discrete version of the plates complex, an exact Hilbert complex relevant for the mixed formulation of fourth-order problems. The derivation of the discrete complex follows the discrete de Rham paradigm, leading to an arbitrary-order construction that applies to meshes composed of general polygonal elements. The discrete plates complex is then used to derive a novel numerical scheme for Kirchhoff-Love plates, for which a full stability and convergence analysis are performed. Ex-tensive numerical tests complete the exposition.

引用

页码：51 / 77

页数：27

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