TY - JOUR

T1 - An adaptive mesh refinement strategy for finite element solution of the elliptic problem

AU - Aulisa, E.

AU - Ke, G.

AU - Lee, S. Y.

N1 - Publisher Copyright:
© 2018 Elsevier Ltd

PY - 2018/7/15

Y1 - 2018/7/15

N2 - In this paper we develop an adaptive finite element method for elliptic problems. First, we assume that in each subdomain the norm of the approximation error at the current mesh configuration is bounded by the norm of the approximation error obtained at the previous mesh configuration, for some norm Hs. Then an a-posteriori error estimator is designed based on the approximate solution correction between the solution on the last two mesh configurations. Based on this new error estimator, the element-wise refinement strategy in each subdomain is provided for a given tolerance. A discussion on the choice of the coefficients in the assumption is given for different norm spaces and for different degrees of finite element family. Four 2D numerical benchmark examples of different domains and two 3D numerical benchmark examples are tested to demonstrate the robustness of our method. When possible, our numerical results are also compared to corresponding results from existing methods. All the results show that the proposed method is robust and efficient in terms of the number of degrees of freedom.

AB - In this paper we develop an adaptive finite element method for elliptic problems. First, we assume that in each subdomain the norm of the approximation error at the current mesh configuration is bounded by the norm of the approximation error obtained at the previous mesh configuration, for some norm Hs. Then an a-posteriori error estimator is designed based on the approximate solution correction between the solution on the last two mesh configurations. Based on this new error estimator, the element-wise refinement strategy in each subdomain is provided for a given tolerance. A discussion on the choice of the coefficients in the assumption is given for different norm spaces and for different degrees of finite element family. Four 2D numerical benchmark examples of different domains and two 3D numerical benchmark examples are tested to demonstrate the robustness of our method. When possible, our numerical results are also compared to corresponding results from existing methods. All the results show that the proposed method is robust and efficient in terms of the number of degrees of freedom.

KW - Adaptive finite element method

KW - a-posteriori error estimator

UR - http://www.scopus.com/inward/record.url?scp=85047210047&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2018.04.011

DO - 10.1016/j.camwa.2018.04.011

M3 - Article

AN - SCOPUS:85047210047

SN - 0898-1221

VL - 76

SP - 224

EP - 244

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 2

ER -