In this work, the authors introduce a generalized weak Galerkin (gWG) finite element method for the time-dependent Oseen equation. The generalized weak Galerkin method is based on a new framework for approximating the gradient operator. Both a semi-discrete and a fully-discrete numerical scheme are developed and analyzed for their convergence, stability, and error estimates. A generalized {\em{inf-sup}} condition is developed to assist the convergence analysis. The backward Euler discretization is employed in the design of the fully-discrete scheme. Error estimates of optimal order are established mathematically, and they are validated numerically with some benchmark examples.
翻译:在这项工作中,作者对基于时间的奥西恩等式采用了普遍薄弱的Galerkin(gWG)有限要素方法。普遍薄弱的Galerkin方法基于一个接近梯度操作员的新框架。制定并分析了半分解和完全分解的数字方法,以了解其趋同、稳定性和误差估计。制定了普遍化的 em{inf-sup}(gWG) 条件,以帮助进行趋同分析。在设计完全分解的方案时采用了落后的Euler分解法。最佳秩序的错误估计是用数学方法确定的,并且用一些基准实例对数字加以验证。