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.
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Habibi, N., & Mesforush, A. (2021). Extending a new two-grid waveform relaxation on a spatial finite element discretization. Computational Methods for Differential Equations, 9(4), 1148-1162. doi: 10.22034/cmde.2020.37349.1653
MLA
Noora Habibi; Ali Mesforush. "Extending a new two-grid waveform relaxation on a spatial finite element discretization". Computational Methods for Differential Equations, 9, 4, 2021, 1148-1162. doi: 10.22034/cmde.2020.37349.1653
HARVARD
Habibi, N., Mesforush, A. (2021). 'Extending a new two-grid waveform relaxation on a spatial finite element discretization', Computational Methods for Differential Equations, 9(4), pp. 1148-1162. doi: 10.22034/cmde.2020.37349.1653
VANCOUVER
Habibi, N., Mesforush, A. Extending a new two-grid waveform relaxation on a spatial finite element discretization. Computational Methods for Differential Equations, 2021; 9(4): 1148-1162. doi: 10.22034/cmde.2020.37349.1653
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