Numerical homogenization is a methodology for the computational solution of multiscale
partial differential equations. It aims at reducing complex large-scale problems to simplified …

The objective of this book is to introduce the reader to the Localized Orthogonal
Decomposition (LOD) method for solving partial differential equations with multiscale data …

We investigate an energy-based formulation of the two-field poroelasticity model and the
related multiple-network model as they appear in geosciences or medical applications. We …

Explicit time step** schemes are popular for linear acoustic and elastic wave propagation
due to their simple nature which does not require sophisticated solvers for the inversion of …

In this paper, we consider the numerical solution of the poroelasticity problem with stochastic
properties. We present a Two-stage Markov Chain Monte Carlo method for geomechanical …

In this work, we employ the Constraint Energy Minimizing Generalized Multiscale Finite
Element Method (CEM-GMsFEM) to solve the problem of linear heterogeneous …

We present a space-time multiscale method for a parabolic model problem with an
underlying coefficient that may be highly oscillatory with respect to both the spatial and the …

In this thesis, we consider the numerical approximation of solutions of partial differential
equations that exhibit some kind of multiscale features. Such equations describe, for …

We prove first-order convergence of the semi-explicit Euler scheme combined with a finite
element discretization in space for elliptic-parabolic problems which are weakly coupled …

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 …