Numerical Solutions of Quasilinear Parabolic Problems by a Continuous Space-Time Finite Element Scheme

Abstract

In this paper, continuous space-time finite element methods are developed for approximating a class of quasilinear parabolic problems in space and in time, simultaneously. The basis of the whole approach is on a space-time variational formulation where streamline upwind terms and interface jump terms are further added for stabilizing the discretization in the direction of time. Error estimates are shown and are verified numerically through a series of numerical tests. Emphasis is placed on investigating the asymptotic convergence of the error parts, which are related to the time discretization.