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A novel efficient mixed formulation for strain‐gradient models
Author(s) -
Papanicolopulos StefanosAldo,
Gulib Fahad,
Marinelli Aikaterini
Publication year - 2018
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.5985
Subject(s) - robustness (evolution) , finite element method , computer science , boundary value problem , mathematical optimization , mathematics , engineering , structural engineering , mathematical analysis , biochemistry , chemistry , gene
Summary Various finite elements based on mixed formulations have been proposed for the solution of boundary value problems involving strain‐gradient models. The relevant literature, however, does not provide details on some important theoretical aspects of these elements. In this work, we first present the existing elements within a novel, single mathematical framework, identifying some theoretical issues common to all of them that affect their robustness and numerical efficiency. We then proceed to develop a new family of mixed elements that addresses these issues while being simpler and computationally cheaper. The behavior of the new elements is further demonstrated through two numerical examples.