Lakkis_Mousavi-nondivergence-IMAJNA-ES2019183-v4-210407.pdf (1.24 MB)
A least-squares Galerkin approach to gradient and Hessian recovery for nondivergence-form elliptic equations
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.
Funding
ModCompShock - Modelling and Computation for Shocks and Interfaces; G1718; EUROPEAN UNION; 642768
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Publication status
- Published
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- Accepted version
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IMA Journal of Numerical AnalysisISSN
0272-4979Publisher
Oxford University PressExternal DOI
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- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2021-04-12First Open Access (FOA) Date
2022-09-10First Compliant Deposit (FCD) Date
2021-04-11Usage metrics
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