Semi-Algebraic mode analysis for finite element discretisations of the heat equation

Document Type : Research Paper


1 Faculty of Applied Mathematics, Shahrood University Of Technology, P.O. Box 3619995161, Shahrood, Iran.

2 Department of Applied Mathematics, Science Faculty, University of Zaragoza, Pedro Cerbuna, 12, 50009 Zaragoza, Spain.

3 Department of Applied Mathematics, School of Engineering and Architecture, University of Zaragoza, Maria de Luna, 3, 50018, Zaragoza, Spain.


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.