Dual least-squares finite element method with stabilization

Eunjung Lee, Hyesun Na

Research output: Contribution to journalArticlepeer-review


The LL*-method is a least-squares finite element approach producing an approximation by solving dual problem corresponding to the given partial differential equations. Due to the unique structure of LL* approximation, it has advantages if the problem has low regularities and when L2-approximation needs to be established. As a drawback, piecewise polynomial type approximation often generates artifacts such as spurious oscillations near where shocks or discontinuities occur in solution. Allowing discontinuous piecewise polynomial approximation in LL* seems to exacerbate this trouble. This paper presents a stabilized LL*-method that is designed to effectively reduce these oscillatory behavior. The consistency and error convergence of proposed method are analyzed and numerical examinations are performed.

Original languageEnglish
JournalNumerical Methods for Partial Differential Equations
Publication statusAccepted/In press - 2023

Bibliographical note

Funding Information:
This work was supported by the laboratory of computational electromagnetics for large‐scale stealth platform (UD200047JD).

Publisher Copyright:
© 2023 Wiley Periodicals LLC.

All Science Journal Classification (ASJC) codes

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics


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