A Super-Convergence Strategy for Two-Dimensional FEM Based on Element Energy Projection Technique

作者：Yuan, S.; Wu, Y.; Xu, J.; Yuan, Z.; Xing, Q.; Ye, Kangsheng^*

来源：Journal of Nanoelectronics and Optoelectronics, 2017, 12(11): 1284-1294.

DOI：10.1166/jno.2017.2272

• Element Energy Projection
• FEM
• Super-Convergence
• Displacements and Derivatives
• 2D Poisson Equation

This paper presents a super-convergence strategy for finite element (FE) analysis of two-dimensional (2D) problems based on the recently proposed Element Energy Projection (EEP) technique, which has been successfully applied to various one-dimensional (1D) problems. A progress for the extension of the 1D-based EEP method to 2D problems has been achieved by considering the 2D FE discretization as an equivalent two steps of successive 1D discretization, for each step of which an associated EEP recovery technique has already been well developed. Equipped with the available EEP formulae for each step with some critical modifications, an effective algorithm for 2D FEM is developed which gives super-convergent solutions for both displacements and derivatives at any point on any 2D element. Numerical examples for the 2D Poisson equation are given to demonstrate the validity and effectiveness of the proposed algorithm, which yields super-convergent displacements and derivatives with convergence at least one order higher than the corresponding FE solutions.

• 出版日期2017-11
• 单位中国地震局工程力学研究所; 清华大学