The finite element method for parabolic equations. II. A posteriori error estimation and adaptive approach (Q790598)

In a comprehensive paper [ibid. 40, 339-371 (1982; reviewed above)] the authors describe and analyse the use of a posteriori error estimation and mesh adaptation in the solution of parabolic partial differential equations. Finite element discretization of the space variables is used to reduced the partial differential equation to a system of ordinary differential equations. In order to achieve a given level of accuracy the space mesh is modified adaptively. Discontinuous mesh changes are allowed at a set of prescribed times. The paper contains both theoretical results and a description of how the mesh changes can be made in accordance with a posteriori estimates in the context of a general linear parabolic problem with one space dimension.