A novel efficient mixed formulation for strain-gradient models

Stefanos Papanicolopulos, Fahad Gulib, Aikaterini Marinelli

Research output: Contribution to journalArticlepeer-review


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 behaviour of the new elements is further demonstrated through a numerical example.
Original languageEnglish
Pages (from-to)926-937
JournalInternational Journal for Numerical Methods in Engineering
Issue number8
Early online date6 Nov 2018
Publication statusPublished - 24 Feb 2019


  • Strain-gradient models
  • Finite element method
  • mixed formulation
  • penalty formulation


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