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

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • 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)

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.

Suggested Citation

  • Igor Mozolevski & Endre Süli & Paulo Rafael Bösing, 2006. "Discontinuous Galerkin Finite Element Method for a Fourth-Order Nonlinear Elliptic Equation Related to the Two-Dimensional Navier-Stokes Equations," Springer Books, in: Alfredo Bermúdez de Castro & Dolores Gómez & Peregrina Quintela & Pilar Salgado (ed.), Numerical Mathematics and Advanced Applications, pages 457-464, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-34288-5_41
    DOI: 10.1007/978-3-540-34288-5_41
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