This article surveys a general approach to error control and adaptive mesh design in
Galerkin finite element methods that is based on duality principles as used in optimal …

This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems
are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit …

In this paper we consider (hierarchical, Lagrange) reduced basis approximation and a
posteriori error estimation for linear functional outputs of affinely parametrized elliptic …

Two decades ago when we wrote Spectral Methods in Fluid Dynamics (1988), the subject
was still fairly novel. Motivated by the many favorable comments we have received and the …

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This work deals with the investigation of bifurcating fluid phenomena using a reduced order
modelling setting aided by artificial neural networks. We discuss the POD-NN approach …

We present a technique for the evaluation of linear‐functional outputs of parametrized
elliptic partial differential equations in the context of deployed (in service) systems. Deployed …

In this paper we review the basic concepts to obtain a posteriori error estimates for the finite
element solution of an elliptic linear model problem. We give the basic ideas to establish …

This paper is an overview of known and new results about the coupling of Navier-Stokes
and Darcy equations to model the filtration of incompressible fluids through porous media …

Engineering analysis requires the prediction of (say, a single) selected “output” se relevant
to ultimate component and system performance:* typical outputs include energies and …