Quasistatic Porous-Thermoelastic Problems: An a Priori Error Analysis

Jacobo Baldonedo, José R. Fernández and José A. López-Campos
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Jacobo Baldonedo: CINCTEX, Departamento de Ingeniería Mecánica, Universidade de Vigo, Máquinas y Motores Térmicos y Fluídos, 36310 Vigo, Spain
José R. Fernández: Departamento de Matemática Aplicada I, Universidade de Vigo, 36310 Vigo, Spain
José A. López-Campos: CINCTEX, Departamento de Ingeniería Mecánica, Universidade de Vigo, Máquinas y Motores Térmicos y Fluídos, 36310 Vigo, Spain

Mathematics, 2021, vol. 9, issue 12, 1-13

Abstract: In this paper, we deal with the numerical approximation of some porous-thermoelastic problems. Since the inertial effects are assumed to be negligible, the resulting motion equations are quasistatic. Then, by using the finite element method and the implicit Euler scheme, a fully discrete approximation is introduced. We prove a discrete stability property and a main error estimates result, from which we conclude the linear convergence under appropriate regularity conditions on the continuous solution. Finally, several numerical simulations are shown to demonstrate the accuracy of the approximation, the behavior of the solution and the decay of the discrete energy.

Keywords: porosity; thermoelasticity; finite elements; a priori error estimates; discrete stability; numerical behavior (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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