Virtual element method for nonlinear convection–diffusion–reaction equation on polygonal meshes
M. Arrutselvi, E. Natarajan
Abstract
In this paper, we discuss the virtual element formulation for the nonlinear convection–diffusion–reaction equation. We consider the Streamline upwind Petrov–Galerkin stabilization to reduce the non-physical oscillations presented in the solution. The nonlinear term is evaluated after a suitable modification with the help of a polynomial projection operator. We perform the error analysis by showing the existence of the solution and derive the convergence estimates in the energy norm. Numerical experiments are conducted in order to validate the theoretical results.
Topics & Concepts
MathematicsPolygon meshConvection–diffusion equationNonlinear systemGalerkin methodApplied mathematicsNorm (philosophy)Finite element methodConvergence (economics)Upwind schemeMathematical analysisProjection (relational algebra)PolynomialDiscontinuous Galerkin methodConvectionAlgorithmGeometryMechanicsThermodynamicsEconomicsPolitical scienceQuantum mechanicsPhysicsEconomic growthLawDiscretizationAdvanced Numerical Methods in Computational MathematicsAdvanced Mathematical Modeling in EngineeringNumerical methods in engineering