CIP-stabilized virtual elements for diffusion-convection-reaction problems
L. Beirão da Veiga, Carlo Lovadina, Manuel Trezzi
Abstract
Abstract The Virtual Element Method (VEM) for diffusion-convection-reaction problems is considered. In order to design a quasi-robust scheme also in the convection-dominated regime, a Continuous Interior Penalty approach is employed. Due to the presence of polynomial projection operators, typical of the VEM, the stability and the error analysis requires particular care—especially in treating the advective term. Some numerical tests are presented to support the theoretical results.
Topics & Concepts
MathematicsDiffusionConvectionReaction–diffusion systemConvection–diffusion equationApplied mathematicsMechanicsMathematical analysisThermodynamicsPhysicsAdvanced Numerical Methods in Computational MathematicsAdvanced Mathematical Modeling in EngineeringNumerical methods for differential equations