an:05982895
Zbl 1227.76047
Burman, Erik
Consistent SUPG-method for transient transport problems: stability and convergence
EN
Comput. Methods Appl. Mech. Eng. 199, No. 17-20, 1114-1123 (2010).
00259486
2010
j
76M20 76M10 76R99 65M12
SUPG; time discretization; Crank-Nicolson; backward Euler; stability; convergence
Summary: We consider the time/space discretization of the transient advection equation. Discretization in space is performed by the streamline upwind Petrov-Galerkin method and in time we use an \(\mathcal A\)-stable finite difference operator. The formulation is strongly consistent in the sense that the time derivative is included in the stabilization term. Uniform stability of the general formulation is proved under a regularity condition on data, or a moderate inverse CFL-condition that allows for optimal choices of the discretization parameters. Both the backward Euler method (BDF1), the Crank-Nicolson scheme and the second-order backward differentiation formula (BDF2) enter the framework and quasi-optimal convergence is proved for these schemes.