A nonsingular-kernel Dirichlet-to-Dirichlet mapping method for the exterior Stokes problem

IF 1.7 3区 数学 Q2 MATHEMATICS, APPLIED Advances in Computational Mathematics Pub Date : 2024-12-18 DOI:10.1007/s10444-024-10216-6
Xiaojuan Liu, Maojun Li, Tao Yin, Shangyou Zhang
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Abstract

This paper studies the finite element method for solving the exterior Stokes problem in two dimensions. A nonlocal boundary condition is defined using a nonsingular-kernel Dirichlet-to-Dirichlet (DtD) mapping, which maps the Dirichlet data on an interior circle to the Dirichlet data on another circular artificial boundary based on the Poisson integral formula of the Stokes problem. The truncated problem is then solved using the MINI-element method and a simple DtD iteration strategy, resulting into a sequence of unique and geometrically (h- independent) convergent solutions. The quasi-optimal error estimate is proved for the iterative solution at the end of the iteration process. Numerical experiments are presented to demonstrate the accuracy and efficiency of the proposed method.

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CiteScore
3.00
自引率
5.90%
发文量
68
审稿时长
3 months
期刊介绍: Advances in Computational Mathematics publishes high quality, accessible and original articles at the forefront of computational and applied mathematics, with a clear potential for impact across the sciences. The journal emphasizes three core areas: approximation theory and computational geometry; numerical analysis, modelling and simulation; imaging, signal processing and data analysis. This journal welcomes papers that are accessible to a broad audience in the mathematical sciences and that show either an advance in computational methodology or a novel scientific application area, or both. Methods papers should rely on rigorous analysis and/or convincing numerical studies.
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