Moving finite element methods for evolutionary problems. I: Theory (Q1116304)

The authors present a unified theory of moving and fixed finite element methods for evolutionary problems of the form \(u_ t=L(u)\) where L is a spatial operator that may be nonlinear. They pay particular attention to the required projections, to problems in one space dimension with hat functions as basis functions, to conservation laws and to the discrete modelling of shocks. They also discuss discretization in time of the resulting system of ordinary differential equations, higher order operators, higher order basis functions, multidimensional problems, the incorporation of boundary conditions, and systems of partial differential equations.