Coupled variational formulations of linear elasticity and the DPG methodology

JOURNAL OF COMPUTATIONAL PHYSICS

卷:348

Article

Fuentes, Federico¹  Keith, Brendan¹  Demkowicz, Leszek¹  Le Tallec, Patrick² 

[1] Univ Texas Austin, ICES, 201 E 24th St, Austin, TX 78712 USA

[2] Ecole Polytech, Lab Mech Solides, Route Saclay, F-91128 Palaiseau, France

关键词: Discontinuous Petrov-Galerkin methodology;    Linear elasticity;    Coupled problem;    High material contrast;    Incompressible material;    Finite element method;    Variational formulation;   

DOI  :  10.1016/j.jcp.2017.07.051

来源: Elsevier

【 摘 要 】

This article presents a general approach akin to domain-decomposition methods to solve a single linear PDE, but where each subdomain of a partitioned domain is associated to a distinct variational formulation coming from a mutually well-posed family of brokenvariational formulations of the original PDE. It can be exploited to solve challenging problems in a variety of physical scenarios where stability or a particular mode of convergence is desired in a part of the domain. The linear elasticity equations are solved in this work, but the approach can be applied to other equations as well. The broken variational formulations, which are essentially extensions of more standard formulations, are characterized by the presence of mesh-dependent broken test spaces and interface trial variables at the boundaries of the elements of the mesh. This allows necessary information to be naturally transmitted between adjacent subdomains, resulting in coupledvariational formulations which are then proved to be globally well-posed. They are solved numerically using the DPG methodology, which is especially crafted to produce stable discretizations of broken formulations. Finally, expected convergence rates are verified in two different and illustrative examples. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free