- - - Faculty of Applied Mathematics, Shahrood University Of Technology, P.O. Box ۳۶۱۹۹۹۵۱۶۱, Shahrood, Iran.
- - - Faculty of Applied Mathematics, Shahrood University Of Technology, P.O. Box ۳۶۱۹۹۹۵۱۶۱, Shahrood, Iran.
- - - Department of Applied Mathematics, Science Faculty, University of Zaragoza, Pedro Cerbuna, ۱۲, ۵۰۰۰۹ Zaragoza, Spain.
- - - Department of Applied Mathematics, School of Engineering and Architecture, University of Zaragoza, Maria de Luna, ۳, ۵۰۰۱۸, 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.

finite element method, Waveform relaxation method, Multigrid technique, Semi-Algebraic Mode Analysis