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http://hdl.handle.net/10397/93878
Title: | Convergence of a second-order energy-decaying method for the viscous rotating shallow water equation | Authors: | Akrivis, G Li, B Wang, J |
Issue Date: | 2021 | Source: | SIAM journal on numerical analysis, 2021, v. 59, no. 1, p. 265-288 | Abstract: | An implicit energy-decaying modified Crank-Nicolson time-stepping method is constructed for the viscous rotating shallow water equation on the plane. Existence, uniqueness, and convergence of semidiscrete solutions are proved by using Schaefer's fixed point theorem and H2 estimates of the discretized hyperbolic-parabolic system. For practical computation, the semidiscrete method is further discretized in space, resulting in a fully discrete energy-decaying finite element scheme. A fixed-point iterative method is proposed for solving the nonlinear algebraic system. The numerical results show that the proposed method requires only a few iterations to achieve the desired accuracy, with second-order convergence in time, and preserves energy decay well. | Keywords: | Energy decay Error estimate Modified Crank-Nicolson Viscous shallow water equation |
Publisher: | Society for Industrial and Applied Mathematics | Journal: | SIAM journal on numerical analysis | ISSN: | 0036-1429 | EISSN: | 1095-7170 | DOI: | 10.1137/20M1328051 | Rights: | © 2021 Society for Industrial and Applied Mathematics The following publication Akrivis, G., Li, B., & Wang, J. (2021). Convergence of a second-order energy-decaying method for the viscous rotating shallow water equation. SIAM Journal on Numerical Analysis, 59(1), 265-288 is available at https://doi.org/10.1137/20M1328051 |
Appears in Collections: | Journal/Magazine Article |
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