Downloads provided by UsageCountsOn existence and numerical approximation in phase-lag thermoelasticity with two temperatures
Copyright policy ) Campo, Marco; Copetti, Maria; Fernández, Jose R.; Quintanilla de Latorre, Ramón;
On existence and numerical approximation in phase-lag thermoelasticity with two temperatures
<p style='text-indent:20px;'>In this work we study from both variational and numerical points of view a thermoelastic problem which appears in the dual-phase-lag theory with two temperatures. An existence and uniqueness result is proved in the general case of different Taylor approximations for the heat flux and the inductive temperature. Then, in order to provide the numerical analysis, we restrict ourselves to the case of second-order approximations of the heat flux and first-order approximations for the inductive temperature. First, variational formulation of the corresponding problem is derived and an energy decay property is proved. Then, a fully discrete scheme is introduced by using the finite element method for the approximation of the spatial variable and the implicit Euler scheme for the discretization of the time derivatives. A discrete stability</p>
Finite elements, Classificació AMS::74 Mechanics of deformable solids::74H Dynamical problems, Classificació AMS::80 Classical thermodynamics, :Matemàtiques i estadística::Matemàtica aplicada a les ciències [Àrees temàtiques de la UPC], Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, numerical simulations, Classificació AMS::65 Numerical analysis::65M Partial differential equations, Finite difference methods for initial value and initial-boundary value problems involving PDEs, initial value and time-dependent initial-boundary value problems, Numerical simulations, Classificació AMS::65 Numerical analysis::65M Partial differential equations, initial value and time-dependent initial-boundary value problems, :35 Partial differential equations::35Q Equations of mathematical physics and other areas of application [Classificació AMS], :65 Numerical analysis::65M Partial differential equations, initial value and time-dependent initial-boundary value problems [Classificació AMS], :80 Classical thermodynamics, heat transfer::80A Thermodynamics and heat transfer [Classificació AMS], A priori estimates, Diffusive and convective heat and mass transfer, heat flow, Existence problems for PDEs: global existence, local existence, non-existence, Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness, Finite difference methods applied to problems in solid mechanics, Phase-lag thermoelasticity, Thermal effects in solid mechanics, Error bounds for initial value and initial-boundary value problems involving PDEs, finite elements, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Termoelasticitat, existence and uniqueness, Elements finits, :74 Mechanics of deformable solids::74H Dynamical problems [Classificació AMS], Finite element method, Finite element methods applied to problems in solid mechanics, a priori estimates, Mètode dels, Smoothness and regularity of solutions to PDEs, phase-lag thermoelasticity, Elements finits, Mètode dels, Existence and uniqueness, Variational methods applied to PDEs, Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics, Thermoelasticity, A priori estimates in context of PDEs, Classificació AMS::80 Classical thermodynamics, heat transfer::80A Thermodynamics and heat transfer, Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències, heat transfer::80A Thermodynamics and heat transfer, PDEs in connection with mechanics of deformable solids, Classificació AMS::35 Partial differential equations::35Q Equations of mathematical physics and other areas of application
Finite elements, Classificació AMS::74 Mechanics of deformable solids::74H Dynamical problems, Classificació AMS::80 Classical thermodynamics, :Matemàtiques i estadística::Matemàtica aplicada a les ciències [Àrees temàtiques de la UPC], Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, numerical simulations, Classificació AMS::65 Numerical analysis::65M Partial differential equations, Finite difference methods for initial value and initial-boundary value problems involving PDEs, initial value and time-dependent initial-boundary value problems, Numerical simulations, Classificació AMS::65 Numerical analysis::65M Partial differential equations, initial value and time-dependent initial-boundary value problems, :35 Partial differential equations::35Q Equations of mathematical physics and other areas of application [Classificació AMS], :65 Numerical analysis::65M Partial differential equations, initial value and time-dependent initial-boundary value problems [Classificació AMS], :80 Classical thermodynamics, heat transfer::80A Thermodynamics and heat transfer [Classificació AMS], A priori estimates, Diffusive and convective heat and mass transfer, heat flow, Existence problems for PDEs: global existence, local existence, non-existence, Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness, Finite difference methods applied to problems in solid mechanics, Phase-lag thermoelasticity, Thermal effects in solid mechanics, Error bounds for initial value and initial-boundary value problems involving PDEs, finite elements, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Termoelasticitat, existence and uniqueness, Elements finits, :74 Mechanics of deformable solids::74H Dynamical problems [Classificació AMS], Finite element method, Finite element methods applied to problems in solid mechanics, a priori estimates, Mètode dels, Smoothness and regularity of solutions to PDEs, phase-lag thermoelasticity, Elements finits, Mètode dels, Existence and uniqueness, Variational methods applied to PDEs, Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics, Thermoelasticity, A priori estimates in context of PDEs, Classificació AMS::80 Classical thermodynamics, heat transfer::80A Thermodynamics and heat transfer, Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències, heat transfer::80A Thermodynamics and heat transfer, PDEs in connection with mechanics of deformable solids, Classificació AMS::35 Partial differential equations::35Q Equations of mathematical physics and other areas of application
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