摘要
We study from a numerical point of view a multidimensional problem involving a viscoelastic body with two porous structures.The mechanical problem leads to a linear system of three coupled hyperbolic partial differential equations.Its corresponding variational formulation gives rise to three coupled parabolic linear equations.An existence and uniqueness result,and an energy decay property,are recalled.Then,fully discrete approximations are introduced using the finite element method and the implicit Euler scheme.A discrete stability property and a priori error estimates are proved,from which the linear convergence of the algorithm is derived under suitable additional regularity conditions.Finally,some numerical simulations are performed in one and two dimensions to show the accuracy of the approximation and the behaviour of the solution.
基金
supported by the Ministerio de Economfa y Competitividad under the research project MTM2015-66640-P(with the participation of FEDER)
by the research project PGC2018-096696-B-I00(Ministerio de Ciencia,Innovacion y Universidades,Spain)with the participation of FEDER
supported by the Ministerio de Economfa y Competitividad under the research project"Analisis Matematico de Problemas de la Termomecanica"(MTM2016-74934-P),(AEI/FEDER,UE)
supported by the research project"Analisis Mateinatico Aplicado a la Termomecanica"supported by the Spanish Ministry de Science,Innovation and Universities(PID2019-105118GB-I00,FEDER).
