A strongly conservative hybridizable discontinuous Galerkin method for the coupled time-dependent Navier–Stokes and Darcy problem
Ayçıl Çeşmeli̇oğlu, Jeonghun J. Lee, Sander Rhebergen
Abstract
We present a strongly conservative and pressure-robust hybridizable discontinuous Galerkin method for the coupled time-dependent Navier–Stokes and Darcy problem. We show existence and uniqueness of a solution and present an optimal a priori error analysis for the fully discrete problem when using Backward Euler time stepping. The theoretical results are verified by numerical examples.
Topics & Concepts
UniquenessDiscontinuous Galerkin methodMathematicsDarcy's lawBackward Euler methodTime steppingA priori and a posterioriEuler's formulaApplied mathematicsMathematical analysisStokes problemDarcy–Weisbach equationEuler equationsFinite element methodPorous mediumPhysicsDiscretizationGeotechnical engineeringThermodynamicsPorosityEngineeringPhilosophyEpistemologyNumerical methods for differential equationsAdvanced Numerical Methods in Computational MathematicsDifferential Equations and Numerical Methods