{"title":"Spectral discretization of the time-dependent Navier-Stokes problem with mixed boundary conditions","authors":"M. Abdelwahed, N. Chorfi","doi":"10.1515/anona-2022-0253","DOIUrl":null,"url":null,"abstract":"Abstract In this work, we handle a time-dependent Navier-Stokes problem in dimension three with a mixed boundary conditions. The variational formulation is written considering three independent unknowns: vorticity, velocity, and pressure. We use the backward Euler scheme for time discretization and the spectral method for space discretization. We present a complete numerical analysis linked to this variational formulation, which leads us to a priori error estimate.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":"11 1","pages":"1447 - 1465"},"PeriodicalIF":3.2000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Nonlinear Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/anona-2022-0253","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 4
Abstract
Abstract In this work, we handle a time-dependent Navier-Stokes problem in dimension three with a mixed boundary conditions. The variational formulation is written considering three independent unknowns: vorticity, velocity, and pressure. We use the backward Euler scheme for time discretization and the spectral method for space discretization. We present a complete numerical analysis linked to this variational formulation, which leads us to a priori error estimate.
期刊介绍：
Advances in Nonlinear Analysis (ANONA) aims to publish selected research contributions devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The Journal focuses on papers that address significant problems in pure and applied nonlinear analysis. ANONA seeks to present the most significant advances in this field to a wide readership, including researchers and graduate students in mathematics, physics, and engineering.
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