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Quasi-Newton Iterative Solution of Non-Orthotropic Elliptic Problems in 3D with Boundary Nonlinearity

  • Benjámin Borsos and János Karátson EMAIL logo
Published/Copyright: February 26, 2022

Abstract

We consider the numerical solution of elliptic problems in 3D with boundary nonlinearity, such as arising in stationary heat conduction models. We allow general non-orthotropic materials where the matrix of heat conductivities is a nondiagonal full matrix. The solution approach involves the finite element method (FEM) and Newton type iterations. We develop a quasi-Newton method for this problem, using spectral equivalence to approximate the derivatives. We derive the convergence of the method, and numerical experiments illustrate the robustness and the reduced computational cost.

MSC 2010: 65N30

Funding statement: This research has been supported by the BME NC TKP2020 grant of NKFIH Hungary and also carried out in the ELTE Institutional Excellence Program (1783-3/2018/FEKUTSRAT) supported by the Hungarian Ministry of Human Capacities, and further, it was supported by the Hungarian Scientific Research Fund NKFIH grants SNN125119 and K 137699.

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Received: 2021-11-16
Revised: 2021-12-06
Accepted: 2021-12-13
Published Online: 2022-02-26
Published in Print: 2022-04-01

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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