Work

A Linearized Galerkin Finite Element Method for Non-linear Kirchhoff-type Problem With Boundary Dissipation

Year: 2026

Type: article

Abstract: This work is concerned with a non-linear Kirchhoff-type wave equation with boundary dissipation, motivated by models of elastic vibrations and wave propagation in dissipative media. A linearized Galerkin finite element method to approximate solutions of the problem is developed and analysed. The scheme is constructed in both semi-discrete and fully discrete settings, with rigorous stability and convergence analyses provided. Using inverse inequalities and compactness arguments, unconditional error estimates without restrictions on the mesh grid are established. Numerical experiments are presented to illustrate the theoretical findings, confirming the efficiency and accuracy of the proposed method in capturing the complex dynamics of Kirchhoff-type equations with strong nonlinearity and boundary damping.

Source: Journal of Applied Analysis & Computation

DOI: 10.11948/20260035

Authors: Arielle S. Yonke Nana, Blaise Tchapnda, Mahamat S. Daoussa Haggar, Mohamed Mbehou

Institutions: Université de Yaoundé I, African Institute for Mathematical Sciences, University of N'Djamena

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W7222395643

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Cites: 25

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