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Volume 13, Issue 5
A Discontinuous Galerkin Method with Minimal Dissipation for a Finite-Strain Plate

Qiao Kang & Yan Xu

DOI: 10.4208/aamm.OA-2020-0388

Adv. Appl. Math. Mech., 13 (2021), pp. 1027-1063.

Published online: 2021-06

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  • Abstract

In this paper, we develop and analyze a discontinuous Galerkin (DG) method with minimal dissipation for the static bending problem of a finite-strain plate equation. The equations are deduced from a three-dimensional field equation. So the coupling of the equations and the mixed derivative terms are the barriers during developing discretization schemes. The error estimates of the scheme are proved in detail. Numerical experiments in different circumstances are presented to demonstrate the capabilities of the method.

  • Keywords

Finite-strain, static bending problem, discontinuous Galerkin methods, numerical fluxes, error estimates.

  • AMS Subject Headings

65N30, 35J47, 35G15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-13-1027, author = {Kang , Qiao and Xu , Yan}, title = {A Discontinuous Galerkin Method with Minimal Dissipation for a Finite-Strain Plate}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2021}, volume = {13}, number = {5}, pages = {1027--1063}, abstract = {

In this paper, we develop and analyze a discontinuous Galerkin (DG) method with minimal dissipation for the static bending problem of a finite-strain plate equation. The equations are deduced from a three-dimensional field equation. So the coupling of the equations and the mixed derivative terms are the barriers during developing discretization schemes. The error estimates of the scheme are proved in detail. Numerical experiments in different circumstances are presented to demonstrate the capabilities of the method.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0388}, url = {http://global-sci.org/intro/article_detail/aamm/19253.html} }
TY - JOUR T1 - A Discontinuous Galerkin Method with Minimal Dissipation for a Finite-Strain Plate AU - Kang , Qiao AU - Xu , Yan JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 1027 EP - 1063 PY - 2021 DA - 2021/06 SN - 13 DO - http://doi.org/10.4208/aamm.OA-2020-0388 UR - https://global-sci.org/intro/article_detail/aamm/19253.html KW - Finite-strain, static bending problem, discontinuous Galerkin methods, numerical fluxes, error estimates. AB -

In this paper, we develop and analyze a discontinuous Galerkin (DG) method with minimal dissipation for the static bending problem of a finite-strain plate equation. The equations are deduced from a three-dimensional field equation. So the coupling of the equations and the mixed derivative terms are the barriers during developing discretization schemes. The error estimates of the scheme are proved in detail. Numerical experiments in different circumstances are presented to demonstrate the capabilities of the method.

Kang , Qiao and Xu , Yan. (2021). A Discontinuous Galerkin Method with Minimal Dissipation for a Finite-Strain Plate. Advances in Applied Mathematics and Mechanics. 13 (5). 1027-1063. doi:10.4208/aamm.OA-2020-0388
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