Variational formulation and numerical analysis of linear elliptic equations in nondivergence form with Cordes coefficients

D. Gallistl

Research output: Contribution to journalArticleAcademicpeer-review

14 Citations (Scopus)
17 Downloads (Pure)

Abstract

This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears and Süli [SIAM J. Numer. Anal., 51 (2013), pp. 2088--2106], and the second one is a new symmetric formulation based on a least-squares functional. These formulations enable the use of standard finite element techniques for variational problems in subspaces of $H^2$ as well as mixed finite element methods from the context of fluid computations. Besides the immediate quasi-optimal a priori error bounds, the variational setting allows for a posteriori error control with explicit constants and adaptive mesh-refinement. The convergence of an adaptive algorithm is proved. Numerical results on uniform and adaptive meshes are included.


Original languageEnglish
Pages (from-to)737-757
Number of pages21
JournalSIAM journal on numerical analysis
Volume55
Issue number2
DOIs
Publication statusPublished - 2017
Externally publishedYes

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