Extending a new two-grid waveform relaxation on a spatial finite element discretization

Document Type : Research Paper


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


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.