An hp-version interior penalty discontinuous Galerkin method (DGFEM) for the numerical
solution of second-order elliptic partial differential equations on general computational …

Two decades ago when we wrote Spectral Methods in Fluid Dynamics (1988), the subject
was still fairly novel. Motivated by the many favorable comments we have received and the …

In this paper, we develop the a posteriori error estimation of hp-version interior penalty
discontinuous Galerkin discretizations of elliptic boundary-value problems. Computable …

We propose an hp-version discontinuous Galerkin finite element method for fully nonlinear
second-order elliptic Hamilton--Jacobi--Bellman equations with Cordes coefficients. The …

Nondivergence form elliptic equations with discontinuous coefficients do not generally
possess a weak formulation, thus presenting an obstacle to their numerical solution by …

In this paper, we develop the a posteriori error estimation of mixed discontinuous Galerkin
finite element approximations of the Stokes problem. In particular, we derive computable …

We consider the two-dimensional Helmholtz equation with constant coefficients on a domain
with piecewise analytic boundary, modelling the scattering of acoustic waves at a sound-soft …

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 …

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 …