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Weak‐form element differential method for solving mechanics and heat conduction problems with abruptly changed boundary conditions
Author(s) -
Zheng YongTong,
Gao XiaoWei,
Lv Jun,
Peng HaiFeng
Publication year - 2020
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6379
Subject(s) - finite element method , boundary element method , robustness (evolution) , boundary value problem , boundary knot method , mathematics , method of fundamental solutions , extended finite element method , computer science , mathematical optimization , mathematical analysis , structural engineering , engineering , biochemistry , chemistry , gene
Summary Element differential method (EDM), as a newly proposed numerical method, has been applied to solve many engineering problems because it has higher computational efficiency and it is more stable than other strong‐form methods. However, due to the utilization of strong‐form equations for all nodes, EDM become not so accurate when solving problems with abruptly changed boundary conditions. To overcome this weakness, in this article, the weak‐form formulations are introduced to replace the original formulations of element internal nodes in EDM, which produce a new strong‐weak‐form method, named as weak‐form element differential method (WEDM). WEDM has advantages in both the computational accuracy and the numerical stability when dealing with the abruptly changed boundary conditions. Moreover, it can even achieve higher accuracy than finite element method (FEM) in some cases. In this article, the computational accuracy of EDM, FEM, and WEDM are compared and analyzed. Meanwhile, several examples are performed to verify the robustness and efficiency of the proposed WEDM.