• 제목/요약/키워드: fully discrete approximations

검색결과 12건 처리시간 0.016초

PSEUDOSPECTRAL METHOD FOR THE DAMPED BOUSSINESQ EQUATION

  • Choo, S.M.
    • 대한수학회논문집
    • /
    • 제13권4호
    • /
    • pp.889-901
    • /
    • 1998
  • Numerical approximations by pseudospectral method are obtained for the damped Boussinesq equation which is a modification of the good Boussinesq equation. The consistency and stability of the method are obtained using the extended Lax-Richtmyer equivalence theorem, which imply the convergence of the method. We obtain error estimates of O(h$^{s}$ + k$^2$) for a fully discrete pseudospectral method.

  • PDF

HIGHER ORDER DISCONTINUOUS GALERKIN FINITE ELEMENT METHODS FOR NONLINEAR PARABOLIC PROBLEMS

  • Ohm, Mi Ray;Lee, Hyun Young;Shin, Jun Yong
    • Journal of the Korean Society for Industrial and Applied Mathematics
    • /
    • 제18권4호
    • /
    • pp.337-350
    • /
    • 2014
  • In this paper, we consider discontinuous Galerkin finite element methods with interior penalty term to approximate the solution of nonlinear parabolic problems with mixed boundary conditions. We construct the finite element spaces of the piecewise polynomials on which we define fully discrete discontinuous Galerkin approximations using the Crank-Nicolson method. To analyze the error estimates, we construct an appropriate projection which allows us to obtain the optimal order of a priori ${\ell}^{\infty}(L^2)$ error estimates of discontinuous Galerkin approximations in both spatial and temporal directions.