Error estimation and control are critical ingredients for improving the reliability of
computational simulations. Adjoint-based techniques can be used to both estimate the error …

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

The finite element method has always been a mainstay for solving engineering problems
numerically. The most recent developments in the field clearly indicate that its future lies in …

Offering the only existing finite element (FE) codes for Maxwell equations that support hp
refinements on irregular meshes, Computing with hp-ADAPTIVE FINITE ELEMENTS …

We give an overview of recent developments concerning the use of adjoint methods in two
areas: the a posteriori error analysis of finite element methods for the numerical solution of …

This paper is a short essay on discontinuous Galerkin methods intended for a very wide
audience. We present the discontinuous Galerkin methods and describe and discuss their …

In this paper a recently developed approach for the design of adaptive discontinuous
Galerkin finite element methods is applied to physically relevant problems arising in inviscid …

An anisotropic, unstructured grid adaptive method is presented for improving the accuracy of
functional outputs of viscous, compressible flow simulations for general discretizations. The …

In this paper we present a novel arbitrary high order accurate discontinuous Galerkin (DG)
finite element method on space–time adaptive Cartesian meshes (AMR) for hyperbolic …

This article describes the extension of the arbitrary high-order Discontinuous Galerkin
(ADER-DG) method to treat locally varying polynomial degress of the basis functions, so …