A damped Kačanov scheme for the numerical solution of a relaxed p(x)-Poisson equation

The focus of the present work is the (theoretical) approximation of a solution of the p ( x )-Poisson equation. To devise an iterative solver with guaranteed convergence, we will consider a relaxation of the original problem in terms of a truncation of the nonlinearity from below and from above by u...

Full description

Saved in:
Bibliographic Details
Published inSN partial differential equations and applications Vol. 4; no. 5
Main Author Heid, Pascal
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.10.2023
Subjects
Analysis
Mathematical and Computational Biology
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
Original Paper
Partial Differential Equations
Theoretical
Damped Kačanov scheme
(
Poisson equation
Relaxation method
35J05
47J25
65N30
Online AccessGet full text

Cover

More Information
Summary:The focus of the present work is the (theoretical) approximation of a solution of the p ( x )-Poisson equation. To devise an iterative solver with guaranteed convergence, we will consider a relaxation of the original problem in terms of a truncation of the nonlinearity from below and from above by using a pair of positive cut-off parameters. We will then verify that, for any such pair, a damped Kačanov scheme generates a sequence converging to a solution of the relaxed equation. Subsequently, it will be shown that the solutions of the relaxed problems converge to the solution of the original problem in the discrete setting. Finally, the discrete solutions of the unrelaxed problem converge to the continuous solution. Our work will finally be rounded up with some numerical experiments that underline the analytical findings.
ISSN:2662-2963
2662-2971
DOI:10.1007/s42985-023-00259-7