Coupled variational formulations of linear elasticity and the DPG methodology

Coupled variational formulations of linear elasticity and the DPG methodology

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 broken variational formulations of the original PDE. It can be exploited to solve challenging problems in a variety of physical scenarios where ...

on the effect of linear & non-linear texts on students comprehension and recalling

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On the stability of DPG formulations of transport equations

In this paper we formulate and analyze a Discontinuous Petrov Galerkin formulation of linear transport equations with variable convection fields. We show that a corresponding infinite dimensional mesh-dependent variational formulation, in which besides the principal field also its trace on the mesh skeleton is an unknown, is uniformly stable with respect to the mesh, where the test space is a c...

Conservation laws of linear elasticity in stress formulations

In this paper, we present new conservation laws of linear elasticity which have been discovered. These newly discovered conservation laws are expressed solely in terms of the Cauchy stress tensor, and they are genuine, non-trivial conservation laws that are intrinsically different from the displacement conservation laws previously known. They represent the variational symmetry conditions of com...

Variations Formulations of the Coupled Theory of Linear Thermoelasticity