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

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.
Authors:
 [1] ;  [2] ;  [2]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. University of Leicester, Leicester (United Kingdom)
Publication Date:
OSTI Identifier:
1159207
Report Number(s):
LA-UR-14-27710
DOE Contract Number:
AC52-06NA25396
Resource Type:
Technical Report
Research Org:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING MATHEMATICS; HIGH-ORDER METHOD; UNSTRUCTURED POLYGONAL MESH; VIRTUAL ELEMENT METHOD; DIFFUSION; CONVECTION-DOMINATED; REACTION-DIFFUSION PROBLEM