A least-squares Galerkin approach to gradient and Hessian recovery for nondivergence-form elliptic equations

Lakkis, Omar and Mousavi, Amireh (2021) A least-squares Galerkin approach to gradient and Hessian recovery for nondivergence-form elliptic equations. IMA Journal of Numerical Analysis. ISSN 0272-4979 (Accepted)

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Abstract

We propose a least-squares method involving the recovery of the gradient and possibly the Hessian for elliptic equation in nondivergence form. As our approach is based on the Lax--Milgram theorem with the curl-free constraint built into the target (or cost) functional, the discrete spaces require no inf-sup stabilization. We show that standard conforming finite elements can be used yielding apriori and aposteriori convergnece results. We illustrate our findings with numerical experiments with uniform or adaptive mesh refinement.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
SWORD Depositor: Mx Elements Account
Depositing User: Mx Elements Account
Date Deposited: 12 Apr 2021 08:17
Last Modified: 12 Apr 2021 08:17
URI: http://sro.sussex.ac.uk/id/eprint/98380

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