Convergence analysis of finite element approximations of the Joule heating problem in three spatial dimensions

DOI10.1007/s10543-010-0287-zzbMath1205.80084OpenAlexW2167444957MaRDI QIDQ616171

Mats G. Larson, Axel Målqvist, Michael Holst, Robert Söderlund

Publication date: 7 January 2011

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-010-0287-z

zbMATH Keywords

convergence analysisfinite element methodsJoule heating problem

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer (80M10)

Related Items (6)

Finite element convergence for the Joule heating problem with mixed boundary conditions ⋮ Finite element convergence analysis for the thermoviscoelastic Joule heating problem ⋮ Local null controllability for the thermistor problem ⋮ Optimal error analysis of Galerkin FEMs for nonlinear Joule heating equations ⋮ Optimal error estimates of a lowest-order Galerkin-mixed FEM for the thermoviscoelastic Joule heating equations ⋮ Unconditional optimal error estimates of BDF-Galerkin FEMs for nonlinear thermistor equations

Cites Work

• Finite elements approximation of second order linear elliptic equations in divergence form with right-hand side in \(L^1\)
• L\({}_{\infty}\) stability of finite element approximations to elliptic gradient equations
• Existence of a solution to a coupled elliptic system
• Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus
• Linearly implicit finite element methods for the time-dependent Joule heating problem
• Discretization of coupled heat and electrical diffusion problems by finite-element and finite-volume methods
• EXISTENCE OF FINITE ENERGY SOLUTIONS FOR ELLIPTIC SYSTEMS WITH L¹-VALUED NONLINEARITIES
• Real Interpolation of Sobolev Spaces on Subdomains of Rn
• Elliptic equations with BMO coefficients in Lipschitz domains
• A Finite Element Model for the Time-Dependent Joule Heating Problem
• The Finite Element Approximation of the Nonlinear Poisson–Boltzmann Equation

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