Mathematicsisplayinganevermoreimportant…-ical sciences, provoking a blurring of
boundaries between scienti? c disciplines and a resurgence of interest in the modern as …

This book is an introduction to a family of discontinuous Galerkin (DG) methods applied to
some steady-state and time-dependent model problems. A special effort was made to have …

Weakly enforced Dirichlet boundary conditions are compared with strongly enforced
conditions for boundary layer solutions of the advection–diffusion equation and …

A combination of ideas in least-squares finite element methods with those of hybridized
methods recently led to discontinuous Petrov--Galerkin (DPG) finite element methods. They …

Residual-based a posteriori error estimates were derived within one unifying framework for
lowest-order conforming, nonconforming, and mixed finite element schemes in Carstensen …

A robust a-posteriori error estimator for interior penalty discontinuous Galerkin
discretizations of a stationary convection–diffusion equation is derived. The estimator yields …

An adaptive discontinuous Galerkin finite element method for linear elasticity problems is
presented. We develop an a posteriori error estimate and prove its robustness with respect …

We consider the adjoint-based error estimation and goal-oriented mesh refinement for
single and multiple aerodynamic force coefficients as well as residual-based mesh …

We introduce a residual-based a posteriori error indicator for discontinuous Galerkin
discretizations of H (curl; Ω)-elliptic boundary value problems that arise in eddy current …

We develop the a posteriori error analysis of hp-version interior-penalty discontinuous
Galerkin finite-element methods for a class of second-order quasi-linear elliptic partial …