%0 Journal Article
%T Extending a new two-grid waveform relaxation on a spatial finite element discretization
%J Computational Methods for Differential Equations
%I University of Tabriz
%Z 2345-3982
%A Habibi, Noora
%A Mesforush, Ali
%D 2021
%\ 10/01/2021
%V 9
%N 4
%P 1148-1162
%! Extending a new two-grid waveform relaxation on a spatial finite element discretization
%K Waveform relaxation method
%K finite element method
%K multigrid acceleration
%R 10.22034/cmde.2020.37349.1653
%X In this work, a new two-grid method presented for the elliptic partial differential equations is generalized to the time-dependent linear parabolic partial differential equations. The new two-grid waveform relaxation method uses the numerical method of lines, replacing any spatial derivative by a discrete formula, obtained here by the finite element method. A convergence analysis in terms of the spectral radius of the corresponding two-grid waveform relaxation operator is also developed. Moreover, the efficiency of the presented method and its analysis are tested, applying the twodimensional heat equation.
%U https://cmde.tabrizu.ac.ir/article_12110_e8ca46e81961a8af033c2a47b9f1c556.pdf