Optimal moving grids for time-dependent partial differential equations

Abstract Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations have been proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. We investigate moving grids on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, we report the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of PDE solutions in the least-squares norm.

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