A virtual element discretization for the time dependent Navier–Stokes equations in stream-function formulation
Dibyendu Adak, David Mora, Sundararajan Natarajan, Alberth Silgado
Abstract
In this work, a new Virtual Element Method (VEM) of arbitrary order k ≥ 2 for the time dependent Navier–Stokes equations in stream-function form is proposed and analyzed. Using suitable projection operators, the bilinear and trilinear terms are discretized by only using the proposed degrees of freedom associated with the virtual space. Under certain assumptions on the computational domain, error estimations are derived and shown that the method is optimally convergent in both space and time variables. Finally, to justify the theoretical analysis, four benchmark examples are examined numerically.
Topics & Concepts
MathematicsDiscretizationBilinear interpolationVirtual workProjection (relational algebra)Function spaceFunction (biology)Domain (mathematical analysis)Navier–Stokes equationsDegrees of freedom (physics and chemistry)Applied mathematicsElement (criminal law)Stream functionFinite element methodMathematical analysisAlgorithmCompressibilityVortexEngineeringPhysicsBiologyPolitical scienceThermodynamicsLawAerospace engineeringStatisticsVorticityEvolutionary biologyQuantum mechanicsAdvanced Numerical Methods in Computational MathematicsNumerical methods in engineeringNumerical methods for differential equations