A modified Kačanov iteration scheme with application to quasilinear diffusion models

01/25/2021
by   Pascal Heid, et al.
0

The classical Kačanov scheme for the solution of nonlinear variational problems can be interpreted as a fixed point iteration method that updates a given approximation by solving a linear problem in each step. Based on this observation, we introduce a modified Kačanov method, which allows for (adaptive) damping, and, thereby, to derive a new convergence analysis under more general assumptions and for a wider range of applications. For instance, in the specific context of quasilinear diffusion models, our new approach does no longer require a standard monotonicity condition on the nonlinear diffusion coefficient to hold. Moreover, we propose two different adaptive strategies for the practical selection of the damping parameters involved.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

05/25/2021

An efficient iterative method for solving parameter-dependent and random diffusion problems

This paper develops and analyzes a general iterative framework for solvi...
09/21/2021

Virtual element method for the system of time dependent nonlinear convection-diffusion-reaction equation

In this work, we have discretized a system of time-dependent nonlinear c...
01/05/2020

A local character based method for solving linear systems of radiation diffusion problems

The radiation diffusion problem is a kind of time-dependent nonlinear eq...
06/21/2021

Strong Convergence of a GBM Based Tamed Integrator for SDEs and an Adaptive Implementation

We introduce a tamed exponential time integrator which exploits linear t...
12/23/2020

Theoretical and numerical analysis for a hybrid tumor model with diffusion depending on vasculature

In this work we analyse a PDE-ODE problem modelling the evolution of a G...
04/24/2021

Hermite Polynomial-based Valuation of American Options with General Jump-Diffusion Processes

We present a new approximation scheme for the price and exercise policy ...
11/29/2018

Convergence Analysis of a Cooperative Diffusion Gauss-Newton Strategy

In this paper, we investigate the convergence performance of a cooperati...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.