A mixed formulation of Boussinesq equations: Analysis of nonsingular solutions
A mixed formulation of Boussinesq equations: Analysis of nonsingular solutions
复制标题
Boussinesq 方程的混合表述：非奇异解的分析
作者：
M. Farhloul;S. Nicaise;L. Paquet
本文研究二维区域上Boussinesq方程的混合形式及其数值逼近。本文首先讨论解的存在性和唯一性结果，以及任意解的正则性的描述。然后，该问题近似的混合有限元方法，其中的梯度的速度和温度的梯度，量的实际重要性，被引入作为新的未知数。在非奇异解附近证明了有限元解的存在性和收敛性。最后给出了拟最优误差估计。
This paper is concerned with the mixed formulation of the Boussinesq equations in two-dimensional domains and its numerical approximation. The paper deals first with existence and uniqueness results, as well as the description of the regularity of any solution. The problem is then approximated by a mixed finite element method, where the gradient of the velocity and the gradient of the temperature, quantities of practical importance, are introduced as new unknowns. An existence result for the finite element solution and convergence results are proved near a nonsingular solution. Quasi-optimal error estimates are finally presented.