Topics in matrix analysis
Iterative methods for solving linear systems
Iterative methods for solving linear systems
Monotone Difference Approximations Of BV Solutions To Degenerate Convection-Diffusion Equations
SIAM Journal on Numerical Analysis
Multigrid
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
The asymptotic properties of the spectrum of nonsymmetrically perturbed Jacobi matrix sequences
Journal of Approximation Theory
High-Order Relaxation Schemes for Nonlinear Degenerate Diffusion Problems
SIAM Journal on Numerical Analysis
Preconditioned Implicit Solvers for Nonlinear PDEs in Monument Conservation
SIAM Journal on Scientific Computing
Preconditioned Implicit Solvers for Nonlinear PDEs in Monument Conservation
SIAM Journal on Scientific Computing
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In this paper an implicit numerical method designed for nonlinear degenerate parabolic equations is proposed. A convergence analysis and the study of the related computational cost are provided. In fact, due to the nonlinear nature of the underlying mathematical model, the use of a fixed point scheme is required. The chosen scheme is the Newton method and its convergence is proven under mild assumptions. Every step of the Newton method implies the solution of large, locally structured, linear systems. A special effort is devoted to the spectral analysis of the relevant matrices and to the design of appropriate multigrid preconditioned Krylov methods. Numerical experiments for the validation of our analysis complement this contribution.