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arXiv · 2609.27935

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

A. Mesforush·N. Habibi
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Abstract

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 two-dimensional heat equation.

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A. Mesforush, N. Habibi. 2026-08-22. Extending a new two-grid waveform relaxation on a spatial finite element discretization. https://arxiv.org/abs/2609.27935

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