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

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conference contribution
posted on 2023-06-09, 21:37 authored by Omar LakkisOmar Lakkis, Amireh Mousavi
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.

Funding

ModCompShock - Modelling and Computation for Shocks and Interfaces; G1718; EUROPEAN UNION; 642768

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Numerical Mathematics and Advanced Applications ENUMATH 2019

ISSN

1439-7358

Publisher

Springer

Volume

139

Page range

651-662

Event name

European Numerical Mathematics and Advanced Applications Conference 2019

Event location

The Netherlands

Event type

conference

Event date

30th Sept - 4th Oct 2019

ISBN

9783030558734

Series

Lecture notes in computational science and engineering

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2020-09-22

First Open Access (FOA) Date

2021-08-23

First Compliant Deposit (FCD) Date

2020-09-18

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