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.
|Journal||Numerical Methods for Partial Differential Equations|
|Publication status||Accepted/In press - 2023|
Bibliographical noteFunding Information:
This work was supported by the laboratory of computational electromagnetics for large‐scale stealth platform (UD200047JD).
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All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics