Discontinuous Galerkin Finite Element Method for a Fourth-Order Nonlinear Elliptic Equation Related to the Two-Dimensional Navier-Stokes Equations

Igor Mozolevski (), Endre Süli () and Paulo Rafael Bösing ()
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Igor Mozolevski: Federal University of Santa Catarina, Mathematics Department
Endre Süli: University of Oxford, Computing Laboratory
Paulo Rafael Bösing: IME, University of São Paulo, Department of Applied Mathematics

A chapter in Numerical Mathematics and Advanced Applications, 2006, pp 457-464 from Springer

Abstract: Abstract We develop an hp-version discontinuous Galerkin method for a nonlinear biharmonic equation corresponding to the two-dimensional incompressible Navier-Stokes equations in the stream-function formulation. We linearize the equation and then we solve the resulting linear problem using a combination of the nonsymmetric discontinuous Galerkin finite element method for the biharmonic part of the equation, and a discontinuous Galerkin finite element method with a jumppenalty term for the hyperbolic part of the equation. Numerical experiments are presented to demonstrate the accuracy of the method for a wide range of Reynolds numbers.

Keywords: Reynolds Number; Stokes Equation; Discontinuous Galerkin Method; Biharmonic Equation; Local Discontinuous Galerkin Method (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-34288-5_41

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DOI: 10.1007/978-3-540-34288-5_41

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