Interpolation finite difference schemes on grids locally refined in time
The authors consider a class of finite difference schemes with local grid refinement in time in a part of the domain and analyze their accuracy with the simplest interpolated interface conditions on the boundary of the adaptation domain. On the basis of the maximum principle, it is shown that these schemes converge uniformly in the uniform norm and the rate of convergence is analyzed. Four difference schemes are used to solve numerically a model Dirichlet problem for a second-order parabolic equation on a rectangle, namely, (a) purely implicit scheme using the basic grid, (b) scheme on a finer grid, (c) scheme with local refinement of the time grid within the adaptation domain, and (d) predictor-corrector scheme on the grid with local refinement. It is found that using a refined grid in time produces numerical solutions without loss of accuracy and with considerably smaller computational effort.
scientific article; zbMATH DE number 1563787
scientific article