The Conforming Virtual Element Method for the convection-diffusion-reaction equation with variable coeffcients.

Manzini, Gianmarco¹  Cangiani, Andrea²  Sutton, Oliver² 

[1] Los Alamos National Lab. (LANL), Los Alamos, NM (United States);University of Leicester, Leicester (United Kingdom)

关键词: MATHEMATICS;    HIGH-ORDER METHOD;    UNSTRUCTURED POLYGONAL MESH;    VIRTUAL ELEMENT METHOD;    DIFFUSION;    CONVECTION-DOMINATED;    REACTION-DIFFUSION PROBLEM;   

DOI  :  10.2172/1159207
RP-ID  :  LA-UR-14-27710
PID  :  OSTI ID: 1159207

学科分类：数学（综合）

美国|英语

来源: SciTech Connect

【 摘 要 】

This document describes the conforming formulations for virtual element approximation of the convection-reaction-diffusion equation with variable coefficients. Emphasis is given to construction of the projection operators onto polynomial spaces of appropriate order. These projections make it possible the virtual formulation to achieve any order of accuracy. We present the construction of the internal and the external formulation. The difference between the two is in the way the projection operators act on the derivatives (laplacian, gradient) of the partial differential equation. For the diffusive regime we prove the well-posedness of the external formulation and we derive an estimate of the approximation error in the H¹-norm. For the convection-dominated case, the streamline diffusion stabilization (aka SUPG) is also discussed.