In this paper, a new iterative two-level algorithm is presented for solving the finite element discretization for nonsymmetric or indefinite elliptic problems. The iterative two-level algorithm uses the same coarse space as the traditional two-grid algorithm, but its ``fine space'' uses the higher oder finite element space under the coarse grid. Therefore, the iterative two-level algorithm only needs one grid, and the computational cost is much lower than the traditional iterative two-grid algorithm. Finally, compared with the traditional two-grid algorithm, numerical experiments show that the computational cost is lower to achieve the same convergence order.

翻译：本文介绍了一个新的迭代两级算法,用于解决非对称或无限期椭圆形问题的有限元素分解。迭代两级算法使用与传统的双电网算法相同的粗粗空间,但其“fine space”使用粗格网下较高的奥德限元素空间。因此,迭代两级算法只需要一个网格,计算成本比传统的迭代双电网算法低得多。最后,与传统的双电网算法相比,数字实验表明,实现相同的汇合顺序的计算成本较低。