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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 propose stable variational formulations for certain linear, unsymmetric operators with first
order transport equations in bounded domains serving as the primary focus of this paper …

We continue our theoretical and numerical study on the Discontinuous Petrov–Galerkin
method with optimal test functions in context of 1D and 2D convection-dominated diffusion …

We give an error analysis of the recently developed DPG method applied to solve the
Poisson equation and a convection-diffusion problem. We prove that the method is …

We propose and analyze a discontinuous Petrov--Galerkin (DPG) method for convection-
dominated diffusion problems that provides robust L^2 error estimates for the field variables …

We introduce a DPG method for convection-dominated diffusion problems. The choice of a
test norm is shown to be crucial to achieving robust behavior with respect to the diffusion …

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 …

The central objective of this paper is to develop reduced basis methods for parameter
dependent transport dominated problems that are rigorously proven to exhibit rate-optimal …

Ever since the pioneering work of Ihlenburg and Babuška for the one-dimensional
Helmholtz equation (1995, Comput. Math. Appl., 30, 9–37), a lot of pre-asymptotic analyses …