Iterative two-level algorithm for nonsymmetric or indefinite elliptic problems

TL;DR

This paper introduces an efficient iterative two-level finite element algorithm for nonsymmetric or indefinite elliptic problems, reducing computational costs while maintaining convergence performance.

Contribution

The proposed method uses a higher-order finite element space on the fine level with a single grid, simplifying the traditional two-grid approach.

Findings

Lower computational cost compared to traditional methods

Achieves same convergence order with fewer resources

Validated through numerical experiments

Abstract

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.