University of Tabriz Computational Methods for Differential Equations 2345-3982 9 1 2021 01 01 Semi-Algebraic mode analysis for finite element discretisations of the heat equation 146 158 9946 10.22034/cmde.2019.32018.1549 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. Francisco Gaspar J. L. Department of Applied Mathematics, Science Faculty, University of Zaragoza, Pedro Cerbuna, 12, 50009 Zaragoza, Spain. Carmen Rodrigo Department of Applied Mathematics, School of Engineering and Architecture, University of Zaragoza, Maria de Luna, 3, 50018, Zaragoza, Spain. Journal Article 2019 05 27 In this work, a semialgebraic mode analysis (SAMA) is proposed for investigating the convergence of a multigrid waveform relaxation method applied to the Finite Element (FE) discretization of the heat equation in two and three dimensions. This analysis for finite element methods is more involved and more general than that for Finite Difference (FD) discretizations, since mass matrix must be considered. The proposed analysis results in a very useful tool to study the behaviour of the multigrid waveform relaxation method depending on the parameters of the problem. https://cmde.tabrizu.ac.ir/article_9946_f1ff5049dbae829a3ee717e84f69f921.pdf