University of Tabriz Computational Methods for Differential Equations 2345-3982 9 4 2021 10 01 Extending a new two-grid waveform relaxation on a spatial finite element discretization 1148 1162 12110 10.22034/cmde.2020.37349.1653 EN Noora Habibi Faculty of Applied Mathematics, Shahrood University Of Technology, P.O. Box 3619995161 Shahrood, Iran. Ali Mesforush Faculty of Applied Mathematics, Shahrood University Of Technology, P.O. Box 3619995161 Shahrood, Iran. Journal Article 2019 12 16 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. https://cmde.tabrizu.ac.ir/article_12110_e8ca46e81961a8af033c2a47b9f1c556.pdf