A posteriori error estimates by recovered gradients in parabolic finite element equations
The method of lines is often used to solve initial boundary value problems. Using this method, the problem is first discretized in space and the resulting system of ordinary differential equations is then approximated in time.The authors show that if the time discretization error is sufficienly small, compared to space discretization error then the elliptic averaging techniques work as well for parabolic problems [cf. \textit{S. Ziukas} and \textit{N.-E. Wiberg}, Lect. Notes Pure Appl. Math. 196, 303--314 (1998; Zbl 0903.65078)]. Numerical illustrations in support of the theoretical results are also given.
scientific article; zbMATH DE number 5382747