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

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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 a priori and a posteriori convergence 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: 28 Feb 2022 15:03
URI: http://sro.sussex.ac.uk/id/eprint/98380

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ModCompShock - Modelling and Computation for Shocks and InterfacesG1718EUROPEAN UNION642768