Work

A Galerkin Finite Element Method for a Nonlocal Parabolic System with Nonlinear Boundary Conditions Arising from the Thermal Explosion Theory

Year: 2025

Type: article

Abstract: In this paper, we discuss a class of nonlocal parabolic systems with nonlinear boundary conditions arising from the thermal explosion theory. First, we prove the local existence and uniqueness of the classical solution using the Leray–Schauder fixed-point theorem. Then, we analyze three Galerkin approximations of the system and derive the optimal-order error estimates: O(hr+1) in L2 norm for continuous-time Galerkin approximation, O(hr+1+(Δt)2) in the L2 norm for Crank–Nicolson Galerkin approximation, and O(hr+1+(Δt)2) in both L2 and H1 norms for extrapolated Crank–Nicolson Galerkin approximation.

Source: Mathematics

DOI: 10.3390/math13050861

Authors: Qipeng Guo, Yu Zhang, Baoqiang Yan

Institution: Shandong Normal University

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: National Natural Science Foundation of China