We present an efficient implementation of the double adaptivity algorithm of Cohen et
al.(2012) within the setting of the Petrov–Galerkin method with optimal test functions. We …

At the fully discrete setting, stability of the discontinuous Petrov–Galerkin (DPG) method with
optimal test functions requires local test spaces that ensure the existence of Fortin operators …

We develop and analyze an ultraweak variational formulation for a variant of the Kirchhoff–
Love plate bending model. Based on this formulation, we introduce a discretization of the …

A new finite element method is presented for a general class of singularly perturbed reaction-
diffusion problems-ε^ 2\varDelta u+ bu= f-ε 2 Δ u+ bu= f posed on bounded …

We introduce and analyze a discontinuous Petrov–Galerkin method with optimal test
functions for the heat equation. The scheme is based on the backward Euler time stepping …

This article lays a mathematical foundation for goal-oriented adaptive mesh refinement and
a posteriori error estimation with discontinuous Petrov--Galerkin (DPG) finite element …

In this dissertation, we present a scalable parallel version of hp3D—a finite element (FE)
software for analysis and discretization of complex three-dimensional multiphysics …

We develop and analyze a discontinuous Petrov–Galerkin method with optimal test
functions (DPG method) for a shallow shell model of Koiter type. It is based on a uniformly …

In this work we study a DPG method for an ultra-weak variational formulation of a reaction–
diffusion problem. We improve existing a priori convergence results by sharpening an …

We present a dual finite element method for a singularly perturbed reaction-diffusion
problem. It can be considered a reduced version of the mixed finite element method for …