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

We consider nonlinear algebraic systems resulting from numerical discretizations of
nonlinear partial differential equations of diffusion type. To solve these systems, some …

Finite element methods approximate solutions of partial differential equations by restricting
the problem to a finite dimensional function space. In hp adaptive finite element methods …

We derive energy-norm a posteriori error bounds for an Euler time-stepping method
combined with various spatial discontinuous Galerkin schemes for linear parabolic …

We present a new anisotropic hp-adaptive technique, which can be employed for the
numerical solution of various scientific and engineering problems governed by partial …

In this paper, we develop subspace correction preconditioners for discontinuous Galerkin
(DG) discretizations of elliptic problems with hp-refinement. These preconditioners are …

In this paper, we consider the symmetric interior penalty discontinuous Galerkin (SIPG)
method with piecewise polynomials of degree r≥ 1 for a class of quasi-linear elliptic …

We consider numerical approximations of nonlinear, monotone, and Lipschitz-continuous
elliptic problems, with gradient-dependent or gradient-independent diffusivity. For this …

This paper presents for the first time the derivation of an hp a posteriori error estimator for the
symmetric interior penalty discontinuous Galerkin finite element method for linear elastic …

We derive a robust a posteriori error estimate for hp-adaptive discontinuous Galerkin
discretizations of stationary convection–diffusion equations. We consider one-irregular …