A Local Discontinuous Galerkin Approximation for the<i>p</i>-Navier–Stokes System, Part I: Convergence Analysis
Alex Kaltenbach, Michael Růžička
Abstract
.In the present paper, we propose a local discontinuous Galerkin approximation for fully nonhomogeneous systems of \(p\)-Navier–Stokes type. On the basis of the primal formulation, we prove well-posedness, stability (a priori estimates), and weak convergence of the method. To this end, we propose a new discontinuous Galerkin discretization of the convective term and develop an abstract nonconforming theory of pseudomonotonicity, which is applied to our problem. We also use our approach to treat the \(p\)-Stokes problem.Keywordsdiscontinuous Galerkin\(p\)-Navier–Stokes systemweak convergenceMSC codes76A0535Q3565N3065N1265N15
Topics & Concepts
MathematicsDiscretizationDiscontinuous Galerkin methodGalerkin methodConvergence (economics)A priori and a posterioriStability (learning theory)Applied mathematicsMathematical analysisTerm (time)Navier–Stokes equationsFinite element methodComputer sciencePhysicsQuantum mechanicsEconomic growthEpistemologyEconomicsThermodynamicsMachine learningPhilosophyCompressibilityAdvanced Numerical Methods in Computational MathematicsAdvanced Mathematical Modeling in EngineeringDifferential Equations and Numerical Methods