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

This paper reviews the variational multiscale stabilization of standard finite element methods
for linear partial differential equations that exhibit multiscale features. The stabilization is of …

We introduce a new Petrov-Galerkin multiscale method for the numerical approximation of
the Helmholtz equation with large wave number $\kappa $ in bounded domains in $\mathbb …

In this paper we propose a local orthogonal decomposition method (LOD) for elliptic partial
differential equations with inhomogeneous Dirichlet and Neumann boundary conditions. For …

We present and analyze a pollution-free Petrov–Galerkin multiscale finite element method
for the Helmholtz problem with large wave number κ as a variant of Peterseim (2014). We …

In this paper we present algorithms for an efficient implementation of the Localized
Orthogonal Decomposition method (LOD). The LOD is a multiscale method for the numerical …

We propose a multiscale approach for an elliptic multiscale setting with general unstructured
diffusion coefficients that is able to achieve high-order convergence rates with respect to the …

This paper is devoted to numerical approximations for the wave equation with a multiscale
character. Our approach is formulated in the framework of the Localized Orthogonal …

Offline computation is an essential component in most multiscale model reduction
techniques. However, there are multiscale problems in which offline procedure is insufficient …

This work presents a new methodology for computing ground states of Bose--Einstein
condensates based on finite element discretizations on two different scales of numerical …