Home  | Publications | Hei23a

A Damped Kačanov Scheme for the Numerical Solution of a Relaxed P(x)-Poisson Equation

MCML Authors

Abstract

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.

article

Partial Differential Equations and Applications

4.40. Aug. 2023.

Authors

P. Heid

Links

DOI

Research Area

 A2 | Mathematical Foundations

BibTeXKey: Hei23a

Back to Top