ANALYSIS OF SOME MOVING SPACE-TIME FINITE-ELEMENT METHODS

Two space-time finite element methods for solving time-dependent partial differential equations are defined and analyzed. The methods are based on the use of isoparametric finite elements to implicitly define the time discretization on a moving mesh in the space dimensions. One method allows for adding and deleting knots in a continuous fashion, while the other allows for discontinuous changes in the mesh (static rezone). A detailed convergence analysis for a model parabolic equation, with a possibly large convection term is presented. Here the authors obtain symmetric best approximation error estimates similar to those obtained by Dupont [Math. Comp., 39 (1982), pp. 85-107] for the semidiscrete case.