Three-step Predictor-Corrector Finite Element Schemes for Consolidation Equation

Abstract

An accurate, stable, and efficient three-step predictor-corrector time integration method is considered, for the first time, to obtain numerical solution for the one-dimensional consolidation equation within a finite and spectral element framework. Theoretical order of accuracy and stability conditions are provided. The three-step predictor-corrector time integration method is third-order accurate and shows a larger stability region than the forward Euler method when applied to the one-dimensional consolidation equation. Furthermore, numerical results are in agreement with analytical solutions previously derived by the authors.

Explicit meshfree $${{\varvec{u}}}-{{\varvec{p}}}_\mathbf{\mathrm{w}}$$ solution of the dynamic Biot formulation at large strain

“…Even though, since the explicit predictor-corrector time integration approach, considered in the present research, seems to capture adequately the complex hydromechanical behavior at large strains, there are other explicit time integration strategies (Runge–Kutta schemes, embedded Runge–Kutta schemes, symplectic algorithms, Taylor–Galerkin-based techniques, etc. [ 5 , 16 , 48 ]) with already proven capabilities in other scientific fields that should be also considered.…”