In this paper, we study the adaptive planewave discretization for a cluster of eigenvalues of second-order elliptic partial differential equations. We first design an a posteriori error estimator and prove both the upper and lower bounds. Based on the a posteriori error estimator, we propose an adaptive planewave method. We then prove that the adaptive planewave approximations have the linear convergence rate and quasi-optimal complexity.
翻译:在本文中,我们研究第二阶椭圆部分差分方程的一组二次等离子值的适应性平流波分解法。 我们首先设计一个后端误差估计器, 并验证上下界。 根据后端误差估计器, 我们提出一个适应性平流波方法。 然后我们证明适应性平流波近似具有线性趋同率和准最佳复杂度。