A least-squares Galerkin gradient recovery method for fully nonlinear elliptic equations

Lakkis, Omar and Mousavi, Amireh (2021) A least-squares Galerkin gradient recovery method for fully nonlinear elliptic equations. European Numerical Mathematics and Advanced Applications Conference 2019, The Netherlands, 30th Sept - 4th Oct 2019. Published in: Numerical Mathematics and Advanced Applications ENUMATH 2019. 139 651-662. Springer ISSN 1439-7358 ISBN 9783030558734

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Abstract

We propose a least squares Galerkin based gradient recovery to approximate Dirichlet problems for strong solutions of linear elliptic problems in nondivergence form and corresponding a priori and a posteriori error bounds. This approach is used to tackle fully nonlinear elliptic problems, e.g., Monge–Amp`ere, Hamilton–Jacobi–Bellman, using the smooth (vanilla) and the semismooth Newton linearization. We discuss numerical results, including adaptive methods based on the a posteriori error indicators.

Item Type: Conference Proceedings
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
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Date Deposited: 22 Sep 2020 14:49
Last Modified: 24 Feb 2022 12:49
URI: http://sro.sussex.ac.uk/id/eprint/93858

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Project NameSussex Project NumberFunderFunder Ref
ModCompShock - Modelling and Computation for Shocks and InterfacesG1718EUROPEAN UNION642768