We present equilibrated flux a posteriori error estimates in a unified setting for conforming,
nonconforming, discontinuous Galerkin, and mixed finite element discretizations of the two …

We extend the discontinuous Galerkin framework to a linear second-order elliptic problem
on a compact smooth connected and oriented surface in ℝ 3. An interior penalty (IP) method …

We present a new scheme, the compact discontinuous Galerkin 2 (CDG2) method, for
solving nonlinear convection-diffusion problems together with a detailed comparison to …

We devise and study experimentally adaptive strategies driven by a posteriori error
estimates to select automatically both the space mesh and the polynomial degree in the …

We give an overview of our recent progress in developing a framework for the derivation of
fully computable guaranteed posteriori error bounds for finite element approximation …

We derive a posteriori error estimates for the hybridizable discontinuous Galerkin (HDG)
methods, including both the primal and mixed formulations, for the approximation of a linear …

Interior penalty discontinuous Galerkin (IPDG) methods for second order elliptic boundary
value problems have been derived from a mixed variational formulation of the problem …

In this paper we present a framework for solving two-phase flow problems in porous media.
The discretization is based on a Discontinuous Galerkin method and includes local grid …

We obtain a computable lower bound on the value of the interior penalty parameters
sufficient for the existence of a unique discontinuous Galerkin finite element approximation …

Immersed boundary method (IBM) can easily distinguish fluid and solid regions in the
computational region, thereby the workload of complex grid generation can be reduced. To …