SUPG-stabilized virtual elements for diffusion-convection problems: a robustness analysis
L. Beirão da Veiga, Franco Dassi, Carlo Lovadina, Giuseppe Vacca
Abstract
The objective of this contribution is to develop a convergence analysis for SUPG-stabilized Virtual Element Methods in diffusion-convection problems that is robust also in the convection dominated regime. For the original method introduced in [Benedetto et al. , CMAME 2016] we are able to show an “almost uniform” error bound (in the sense that the unique term that depends in an unfavourable way on the parameters is damped by a higher order mesh-size multiplicative factor). We also introduce a novel discretization of the convection term that allows us to develop error estimates that are fully robust in the convection dominated cases. We finally present some numerical result.
Topics & Concepts
DiscretizationConvectionMathematicsRobustness (evolution)Convection–diffusion equationMultiplicative functionApplied mathematicsFinite element methodTerm (time)Numerical analysisConvergence (economics)Mathematical optimizationMathematical analysisMechanicsPhysicsQuantum mechanicsGeneEconomic growthEconomicsThermodynamicsChemistryBiochemistryAdvanced Numerical Methods in Computational MathematicsAdvanced Mathematical Modeling in EngineeringComputational Fluid Dynamics and Aerodynamics