Affiliation:
1. School of Mathematics and Computing Yonsei University Seoul Republic of Korea
Abstract
AbstractThe 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.
Funder
Agency for Defense Development
Subject
Applied Mathematics,Computational Mathematics,Numerical Analysis,Analysis