A parametric acceleration of multilevel Monte Carlo convergence for nonlinear variably saturated flow

We present a multilevel Monte Carlo (MLMC) method for the uncertainty quantification of variably saturated porous media flow that is modeled using the Richards equation. We propose a stochastic extension for the empirical models that are typically employed to close the Richards equations. This is achieved by treating the soil parameters in...

Multigrid method for nonlinear poroelasticity equations

In this study, a nonlinear multigrid method is applied for solving the system of incompressible poroelasticity equations considering nonlinear hydraulic conductivity. For the unsteady problem, an additional artificial term is utilized to stabilize the solutions when the equations are discretized on collocated grids. We employ two nonlinear...

Accuracy Measures and Fourier Analysis for the Full Multigrid Algorithm

The full multigrid (FMG) algorithm is often claimed to achieve so-called discretization-level accuracy. In this paper, this notion is formalized by defining a worst-case relative accuracy measure, denoted ElFMG, which compares the total error of the l-level FMG solution against the inherent discretization error. This measure can be used for...