【摘要】 <正> 1.引 言 非线性Galerkin方法是一种求解具有耗散项的偏微分方程的近似解的多重水平方法。该方法是将未知量分裂成两项(或多项),它们分别属于具有不同网格尺度的离散空间,在计算过程中,对于“小尺度”的分量引入简化逼近,使得该方法变得很便利。这些方法在Fourier谱离散化和有限元逼近中已有不少的报道。然而在[8]中才首先将非线性Galerkin混合元法与Galerkin/Petrov最小二乘法结合起来(称其为非线性Galerkin/Petrov最小二乘混合元法)用于定常的Navier-Stokes问题。更多还原

【Abstract】 In this paper, a nonlinear Galerkin/Petrov-least squares mixed element (NG-PLSME) method for the stationary conduction-convection problems is presented and analyzed. The method is consistent and stable for any combination of discrete velocity and pressure spaces without requiring the Babuska-Brezzi stability condition. The existence, uniqueness and convergence (at optimal rate) of the NGPLSME solution is proved in the case of sufficient viscosity (or small data).更多还原