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.
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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Articles in the same Issue
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- Multi-Scale Paraxial Models to Approximate Vlasov–Maxwell Equations
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Articles in the same Issue
- Frontmatter
- A General Error Estimate For Parabolic Variational Inequalities
- Functional A Posteriori Error Estimates for the Parabolic Obstacle Problem
- Multi-Scale Paraxial Models to Approximate Vlasov–Maxwell Equations
- Finite Element Penalty Method for the Oldroyd Model of Order One with Non-smooth Initial Data
- Quasi-Newton Iterative Solution of Non-Orthotropic Elliptic Problems in 3D with Boundary Nonlinearity
- Improving Regularization Techniques for Incompressible Fluid Flows via Defect Correction
- Fully Discrete Finite Element Approximation of the MHD Flow
- Sparse Data-Driven Quadrature Rules via ℓ p -Quasi-Norm Minimization
- Identification of Matrix Diffusion Coefficient in a Parabolic PDE
- A Finite Element Method for Two-Phase Flow with Material Viscous Interface
- On the Finite Element Approximation of Fourth-Order Singularly Perturbed Eigenvalue Problems
- Application of Fourier Truncation Method to Numerical Differentiation for Bivariate Functions
- Factorized Schemes for First and Second Order Evolution Equations with Fractional Powers of Operators