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• W2024011917 endingPage "1843" @default.
• W2024011917 startingPage "1797" @default.
• W2024011917 abstract "We prove nonlinear stability and convergence of certain boundary integral methods for time-dependent water waves in a two-dimensional, inviscid, irrotational, incompressible fluid, with or without surface tension. The methods are convergent as long as the underlying solution remains fairly regular (and a sign condition holds in the case without surface tension). Thus, numerical instabilities are ruled out even in a fully nonlinear regime. The analysis is based on delicate energy estimates, following a framework previously developed in the continuous case [Beale, Hou, and Lowengrub, Comm. Pure Appl. Math., 46 (1993), pp. 1269–1301]. No analyticity assumption is made for the physical solution. Our study indicates that the numerical methods must satisfy certain compatibility conditions in order to be stable. Violation of these conditions will lead to numerical instabilities. A breaking wave is calculated as an illustration." @default.
• W2024011917 created "2016-06-24" @default.
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• W2024011917 date "1996-10-01" @default.
• W2024011917 modified "2023-09-27" @default.
• W2024011917 title "Convergence of a Boundary Integral Method for Water Waves" @default.
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• W2024011917 doi "https://doi.org/10.1137/s0036142993245750" @default.
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