论文标题
重建的不连续近似在顺序最小二乘配方中的Stokes方程
Reconstructed Discontinuous Approximation to Stokes Equation in A Sequential Least Squares Formulation
论文作者
论文摘要
我们提出了一种新的最小二乘有限元方法，以通过两个顺序步骤解决Stokes问题。近似空间是通过补丁重建构建的，每个元素一个未知。在第一步中，我们重建一个近似空间，该近似空间由零迹线的分段无卷曲多项式组成。在这个空间中，我们最大程度地减少了最小二项功能的toobtain theumericalApproximation，stothe thevelocity和压力的梯度。在第二步中，我们最大程度地减少了另一个最小二乘功能，从而为重建的无发散空间中的速度提供了解决方案。我们在L2规范和能量规范下得出所有未知数的错误估计。数值在两个维度和三个维度上的结果验证了收敛速率，并证明了我们方法的极大灵活性。
We propose a new least squares finite element method to solve the Stokes problem with two sequential steps. The approximation spaces are constructed by patch reconstruction with one unknown per element. For the first step, we reconstruct an approximation space consisting of piecewise curl-free polynomials with zero trace. By this space, we minimize a least squaresfunctional toobtain thenumericalapproximationstothe gradientof thevelocityand the pressure. In the second step, we minimize another least squares functional to give the solution to the velocity in the reconstructed piecewise divergence-free space. We derive error estimates for all unknowns under L2 norms and energy norms. Numerical results in two dimensions and three dimensions verify the convergence rates and demonstrate the great flexibility of our method.
