arXiv subjects

Weifeng Qiu

Publications and source records attributed to Weifeng Qiu.

40 records · Page 3Linked to original sources

arXiv2012

A locking free hp DPG method for linear elasticity with symmetric stresses

We present two new methods for linear elasticity with simultaneously yield stress and displacement approximations of optimal accuracy in both the mesh size h and polynomial degree p. This is achieved within the recently developed discontinuous Petrov-Galerkin (DPG) framework. In this framework, both the stress and the displacement approximations are discontinuous across element interfaces. We study locking-free convergence properties and the interrelationships between the two DPG methods.

math.NA↗

arXiv2011

Partial expansion of a Lipschitz domain and some applications

We show that a Lipschitz domain can be expanded solely near a part of its boundary, assuming that the part is enclosed by a piecewise C1 curve. The expanded domain as well as the extended part are both Lipschitz. We apply this result to prove a regular decomposition of standard vector Sobolev spaces with vanishing traces only on part of the boundary. Another application in the construction of low-regularity projectors into finite element spaces with partial boundary conditions is also indicated.

math.AP↗

arXiv2010

Variable Order Mixed H-Finite Element Method for Linear Elasticity with Weakly Imposed Symmetry. Ii. Affine and Curvilinear Elements in 2D

We continue our study on variable order Arnold-Falk-Winther elements for 2D elasticity in context of both affine and parametric curvilinear elements. We present an $h$-stability result for affine elements, and an asymptotic stability result for curvilinear elements. Both theoretical results are confirmed with numerical experiments.

math.NA↗

arXiv2010

Mixed hp-finite element method for linear elasticity with weakly imposed symmetry III: Stability analysis in 3D

The paper presents a generalization of Arnold-Falk-Winther elements for three dimensional linear elasticity, to meshes with elements of variable order. The generalization is straightforward but the stability analysis involves a non-trivial modification of involved interpolation operators. The analysis addresses only the h-convergence.

math.NA↗