降阶单元的新进展:内置了最大模误差估计器的自适应有限元法初探

NEW PROGRESS IN REDUCED ELEMENT:AN ADAPTIVE FINITE ELEMENT METHOD WITH BUILT-IN ERROR ESTIMATOR IN MAXIMUM NORM

该文基于初值问题中降阶单元的成功实践,进一步对一般边值问题提出无需超收敛计算、无需结构化网格、无需结点位移修正的降阶单元;进而提出以降阶单元作为最终解,且内置了最大模误差估计器的自适应有限元算法。该文对这一研究进展做简要介绍,并给出一维和二维边值问题的初步算例,以展示本法的可行性、有效性和可靠性。

Based on the successful performance of the reduced element for initial value problems,the reduced element for general boundary value problems is proposed without the needs for super-convergence calculations,structural meshes and nodal accuracy improvement.An adaptive finite element algorithm with the solution of the reduced element and a built-in maximum norm error estimator as the final results is subsequently proposed.This paper gives a brief report to this research progress and provides preliminary numerical examples in one-and twodimensional boundary value problems to exhibit the feasibility,effectiveness and reliability of the proposed algorithm.