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

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Publicado en:Mathematics vol. 13, no. 5 (2025), p. 861
Autor Principal: Guo, Qipeng
Outros autores: Zhang, Yu, Yan, Baoqiang
Publicado:
MDPI AG
Materias:
Boundary conditions
Finite element method
Approximation
Finite element analysis
Partial differential equations
Nonlinear systems
Norms
Galerkin method
Explosions
Fixed points (mathematics)
Schauder fixpoint theorem
Acceso en liña:Citation/Abstract
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Resumo: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: <inline-formula>O(hr+1)</inline-formula> in <inline-formula>L2</inline-formula> norm for continuous-time Galerkin approximation, <inline-formula>O(hr+1+(Δt)2)</inline-formula> in the <inline-formula>L2</inline-formula> norm for Crank–Nicolson Galerkin approximation, and <inline-formula>O(hr+1+(Δt)2)</inline-formula> in both <inline-formula>L2</inline-formula> and <inline-formula>H1</inline-formula> norms for extrapolated Crank–Nicolson Galerkin approximation.
ISSN:2227-7390
DOI:10.3390/math13050861
Fonte:Engineering Database