Approximation of parabolic problems on grids locally refined in time and space Academic Article uri icon

abstract

  • We present a strategy for solving time-dependent problems on grids with local refinement in time and in space, using different time-step sizes in different regions of space. We discuss two approximations based on the discontinuous Galerkin method and the finite difference method with piecewise constant and piecewise linear interpolation in the time direction along the interface between the coarse-and fine-grid regions. Next, we present an iterative method for solving the composite-grid system that is based on domain decomposition techniques and reduces to solution of standard problems with standard time stepping (alternatively on the coarse and fine grids). Finally, numerical results that confirm both the analysis and the convergence theory of the iterative method are presented. © 1994.

author list (cited authors)

  • Ewing, R. E., & Lazarov, R. D.

citation count

  • 11

publication date

  • April 1994