Discrete gradient method over polygon mesh

✍ Scribed by Jia Lu; Jing Qian

• Publisher: John Wiley and Sons
• Year: 2009
• Tongue: English
• Weight: 314 KB
• Volume: 78
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.2498

✦ Synopsis

Abstract

This paper presents a discrete method over domains originally discretized by polygons including triangle, quadrilateral, and general n‐sided polygon elements. In this method, the domain is re‐partitioned into node‐based cells. At each node, the gradient of a physical variable is approximated using a linearly exact discrete operator that involves a set of neighboring nodes. The discrete gradient is subsequently substituted into a weak form to yield a nodal‐integration Galerkin formulation. A unified geometric approach is provided for constructing the gradient operators over an arbitrary polygon mesh. The method does not introduce continuous approximation of the unknown variable; therefore, the numerical computation is very simple. The linear displacement patch test is satisfied by construction. Numerical tests show that the method has comparable accuracy and convergence rate as the displacement finite element method. Examples are also included to illustrate the ability to resist numerical locking in the incompressibility limit and the thin‐element limit. Copyright © 2008 John Wiley & Sons, Ltd.