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

We present a general treatment of the variational multiscale method in the context of an
abstract Dirichlet problem. We show how the exact theory represents a paradigm for subgrid …

The following sections are included: Advances in Mathematical Modelling Dynamics of
Dilute Polymer Solutions The Rouse model Dumbbell models Closure Approximations …

A new finite element method for fourth-order elliptic partial differential equations is presented
and applied to thin bending theory problems in structural mechanics and to a strain gradient …

This chapter presents an introduction to multiscale and stabilized methods, which represent
unified approaches to modeling and numerical solution of fluid dynamic phenomena. Finite …

An improved unusual finite element method is studied herein for a second-order linear
scalar differential equation including a zero-order term. The method consists in subtracting …

The Galerkin method enriched with residual‐free bubbles is considered for approximating
the solution of the Helmholtz equation. Two‐dimensional tests demonstrate the improvement …

We aim at proposing novel stable finite element methods for the mixed Darcy equation with
heterogeneous coefficients within a space splitting framework. We start from the primal …

We further consider the Galerkin method for advective-diffusive equations in two
dimensions. The finite dimensional space employed is of piecewise polynomials enriched …

Die meisten technisch–wissenschaftlichen Problemstellungen und reale Ingenieuraufgaben
gehören genau genommen zur Gruppe sogenannter Mehrfeld–Probleme. Eine bedeutsame …