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

Borsos, Benjámin Richárd and Karátson, János (2022) Quasi-Newton Iterative Solution of Non-Orthotropic Elliptic Problems in 3D with Boundary Nonlinearity. COMPUTATIONAL METHODS IN APPLIED MATHEMATICS, 22 (2). pp. 327-340. ISSN 1609-4840

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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.

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