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http://hdl.handle.net/10397/95651
Title: | Convergence of renormalized finite element methods for heat flow of harmonic maps | Authors: | Gui, X Li, B Wang, J |
Issue Date: | 2022 | Source: | SIAM journal on numerical analysis, 2022, v. 60, no. 1, p. 312-338 | Abstract: | A linearly implicit renormalized lumped mass finite element method is considered for solving the equations describing heat flow of harmonic maps, of which the exact solution naturally satisfies the pointwise constraint |m| = 1. At every time level, the method first computes an auxiliary numerical solution by a linearly implicit lumped mass method and then renormalizes it at all finite element nodes before proceeding to the next time level. It is shown that such a renormalized finite element method has an error bound of O(T+ hr+1) for tensor-product finite elements of degree r ≽ 1. The proof of the error estimates is based on a geometric relation between the auxiliary and renormalized numerical solutions. The extension of the error analysis to triangular mesh is straightforward and discussed in the conclusion section. | Keywords: | Error estimates Finite element methods Heat flow of harmonic maps Lumped mass Renormalization at nodes |
Publisher: | Society for Industrial and Applied Mathematics | Journal: | SIAM journal on numerical analysis | ISSN: | 0036-1429 | EISSN: | 1095-7170 | DOI: | 10.1137/21M1402212 | Rights: | © 2022 Society for Industrial and Applied Mathematics The following publication Gui, X., Li, B., & Wang, J. (2022). Convergence of Renormalized Finite Element Methods for Heat Flow of Harmonic Maps. SIAM Journal on Numerical Analysis, 60(1), 312-338 is available at https://doi.org/10.1137/21M1402212. |
Appears in Collections: | Journal/Magazine Article |
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Gui_Convergence_Renormalized_Finite.pdf | 472.23 kB | Adobe PDF | View/Open |
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