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2021 | OriginalPaper | Chapter

A Least-Squares Galerkin Gradient Recovery Method for Fully Nonlinear Elliptic Equations

Authors : Omar Lakkis, Amireh Mousavi

Published in: Numerical Mathematics and Advanced Applications ENUMATH 2019

Publisher: Springer International Publishing

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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–Ampère, 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.

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previous chapter Assembly of Multiscale Linear PDE Operators

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Omar Lakkis and Amireh Mousavi. A least-squares Galerkin approach to gradient and Hessian recovery for nondivergence-form elliptic equations. online preprint (under peer-review) 1909.00491, arXiv, 09 2019. https://arxiv.org/abs/1909.00491v1.

Omar Lakkis and Amireh Mousavi. A least-squares galerkin approach to gradient recovery for Hamilton-Jacobi-Bellman equations with cordes coefficients. in preparation, 2020.

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Iain Smears and Endre Süli. Discontinuous Galerkin finite element methods for time-dependent Hamilton–Jacobi–Bellman equations with Cordes coefficients. Numerische Mathematik, 133(1):141–176, May 2016. ISSN 0029-599X, 0945-3245. https://doi.org/10.1007/s00211-015-0741-6. http://arxiv.org/abs/1406.4839. arXiv: 1406.4839.

Title: A Least-Squares Galerkin Gradient Recovery Method for Fully Nonlinear Elliptic Equations
Authors: Omar Lakkis
Amireh Mousavi
Publisher: Springer International Publishing
Book: Numerical Mathematics and Advanced Applications ENUMATH 2019
Print ISBN: 978-3-030-55873-4

Electronic ISBN: 978-3-030-55874-1

Copyright Year: 2021
DOI: https://doi.org/10.1007/978-3-030-55874-1_64

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