A Decoupling and Linearizing Discretization for Weakly Coupled Poroelasticity with Nonlinear Permeability
Robert Altmann, Roland Maier
Abstract
We analyze a semiexplicit time discretization scheme of first order for poroelasticity with nonlinear permeability provided that the elasticity model and the flow equation are only weakly coupled. The approach leads to a decoupling of the equations and, at the same time, linearizes the nonlinearity without the need of further inner iteration steps. Hence, the computational speedup is twofold without a loss in the convergence rate. We prove optimal first-order error estimates by considering a related delay system and investigate the method numerically for different examples with various types of nonlinear displacement-permeability relations.
Topics & Concepts
DiscretizationPoromechanicsNonlinear systemMathematicsDecoupling (probability)Elasticity (physics)Applied mathematicsRate of convergenceSpeedupMathematical analysisPorous mediumComputer sciencePhysicsEngineeringControl engineeringComputer networkThermodynamicsOperating systemChannel (broadcasting)Quantum mechanicsGeotechnical engineeringPorosityAdvanced Numerical Methods in Computational MathematicsAdvanced Mathematical Modeling in EngineeringStability and Controllability of Differential Equations