An abstract analysis framework for monolithic discretisations of poroelasticity with application to Hybrid High-Order methods

Autor: Lorenzo Alessio Botti, Daniele Antonio Di Pietro, Michele Botti
Přispěvatelé: Department of Industrial Engineering, University of Bergamo, Laboratorio di Modellistica e Calcolo Scientifico MOX (Dipartimento di Matematica 'Francesco Brioschi'), Politecnico di Milano [Milan] (POLIMI), Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Di Pietro, Daniele Antonio
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Work (thermodynamics)
Discretization
Poromechanics
Stability (learning theory)
010103 numerical & computational mathematics
Weak formulation
01 natural sciences
Abstract analysis framework
Biot problem
Hybrid High-Order methods
Polyhedral meshes
Poroelasticity
abstract analysis framework
Convergence (routing)
[PHYS.MECA.SOLID]Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph]
FOS: Mathematics
Applied mathematics
[PHYS.MECA.MEFL] Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph]
Mathematics - Numerical Analysis
[PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph]
0101 mathematics
High order
Mathematics
[PHYS.MECA.SOLID] Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph]
65N08
65N30
76S05
Biot number
polyhedral meshes
Numerical Analysis (math.NA)
[MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA]
010101 applied mathematics
Computational Mathematics
Computational Theory and Mathematics
Modeling and Simulation
Settore ING-IND/06 - Fluidodinamica
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Popis: In this work, we introduce a novel abstract framework for the stability and convergence analysis of fully coupled discretisations of the poroelasticity problem and apply it to the analysis of Hybrid High-Order (HHO) schemes. A relevant feature of the proposed framework is that it rests on mild time regularity assumptions that can be derived from an appropriate weak formulation of the continuous problem. To the best of our knowledge, these regularity results for the Biot problem are new. A novel family of HHO discretisation schemes is also proposed and analysed, and their performance numerically evaluated.
Databáze: OpenAIRE
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