Some Observations on a Static Spatial Remeshing Method Based on Equidistribution Principles

This paper proposes a method of lines solution procedure with time and space adaptation for one-dimensional systems of partial differential equations whose solutions display steep moving fronts. The spatial remeshing algorithm, which is a variation of the method published by Sanz-Serna and Christie and an extension suggested by Revilla, is a static remeshing method based on equidistribution principles. The selection of the several algorithm components, i.e., grid placement criterion, spatial discretization scheme, time integrator, adaptation frequency, and parameter tuning, are investigated and illustrated with several test examples, i.e., the cubic Schrödinger equation, a model of a single-step reaction with diffusion, and a model of flame propagation.