An Adaptive Discrete Geometric Approach for high-accuracy solutions of 2-D elliptic problems on the coarse grid

Article type: Research Article

Authors: Chen, Feng^* | Wang, Jiawei | Bai, Xubin

Affiliations: State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China

Correspondence: [*] Corresponding author: Feng Chen, State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China. Tel./Fax: +86 029-82668630; E-mail: chenf@mail.xjtu.edu.cn.

Abstract: An Adaptive Discrete Geometric Approach is proposed for high-accuracy simulations of 2-D elliptic problems on the coarse grid. The idea is to reduce the error coming from the discretization of the constitutive equations by using the patch recovery technique. The integration-oriented scheme is adopted for the recovery procedure due to the high-precision of the regression functions. The accuracy and efficiency of the proposed approach are verified by the numerical tests.

Keywords: Discrete Geometric Approach, patch recovery, bicubic spline interpolation, constitutive matrix

DOI: 10.3233/JAE-170082

Journal: International Journal of Applied Electromagnetics and Mechanics, vol. 55, no. 2, pp. 195-203, 2017