A comparison of some adaptive space mesh solvers for the numerical solution of parabolic partial differential equations (Q1913461)

This paper compares a number of numerical solution procedures designed for a broad class of initial value problems modelled as systems of partial differential equations in one space variable. The partial differential equations are of parabolic type, but in some cases are of hyperbolic type, which can be treated numerically as parabolic by adding artificial viscosity corrections. The considered codes use static regridding, finite difference and finite element discretizations for the Lagrangian form of the problem, and a moving finite element method. Some general observations on the relative performances are summarized.