Journal of Scientific Computing

We present this special issue of the Journal of Scientific Computing to celebrate Bernardo Cockburn's sixtieth birthday. The theme of this issue is discontinuous Galerkin methods, a hallmark of Bernardo's distinguished professional career. This foreword ...

In this work, we study advection-robust Hybrid High-Order discretizations of the Oseen equations. For a given integer $$k\geqslant 0$$k?0, the discrete velocity unknowns are vector-valued polynomials of total degree $$\leqslant \, k$$?k on mesh elements ...

In this paper we present efficient quadrature rules for the numerical approximation of integrals of polynomial functions over general polygonal/polyhedral elements that do not require an explicit construction of a sub-tessellation into triangular/...

The present study is concerned with the numerical approximation of periodic solutions of systems of Korteweg---de Vries type, coupled through their nonlinear terms. We construct, analyze and numerically validate two types of schemes that differ in their ...

In this paper, we briefly review some recent developments in the superconvergence of three types of discontinuous Galerkin (DG) methods for time-dependent partial differential equations: the standard DG method, the local discontinuous Galerkin method, ...

We devise a hybrid low-order method for Bingham pipe flows, where the velocity is discretized by means of one unknown per mesh face and one unknown per mesh cell which can be eliminated locally by static condensation. The main advantages are local ...

Using the primal formulation of the Local Discontinuous Galerkin (LDG) method, discrete analogues of the energy and the Hamiltonian of a general class of fractional nonlinear Schrödinger equation are shown to be conserved for two stabilized version of ...

Usual spectral methods are very effective for problems with smooth solutions, but their accuracy will be severely limited if solution of the underlying problems exhibits singular behavior. We develop in this paper enriched spectral-Galerkin methods (ESG)...

Staggered grid techniques have been applied successfully to many problems. A distinctive advantage is that physical laws arising from the corresponding partial differential equations are automatically preserved. Recently, a staggered discontinuous ...

We introduce a continuous (downscaling) data assimilation algorithm for the 2D Bénard convection problem using vorticity or local circulation measurements only. In this algorithm, a nudging term is added to the vorticity equation to constrain the model. ...

This paper is concerned with developing accurate and efficient numerical methods for fully nonlinear second order elliptic and parabolic partial differential equations (PDEs) in multiple spatial dimensions. It presents a general framework for ...

We present the recent development of hybridizable and embedded discontinuous Galerkin (DG) methods for wave propagation problems in fluids, solids, and electromagnetism. In each of these areas, we describe the methods, discuss their main features, ...

We consider the coupling of free and porous media flow governed by Stokes and Darcy equations with the Beavers---Joseph---Saffman interface condition. This model is discretized using a divergence-conforming finite element for the velocities in the whole ...

Ideal magnetohydrodynamic (MHD) equations are widely used in many areas in physics and engineering, and these equations have a divergence-free constraint on the magnetic field. In this paper, we propose high order globally divergence-free numerical ...

In this paper, we prove a discrete embedding inequality for the Raviart---Thomas mixed finite element methods for second order elliptic equations, which is analogous to the Sobolev embedding inequality in the continuous setting. Then, by using the ...

This work proposes a superconvergent hybridizable discontinuous Galerkin (HDG) method for the approximation of the Cauchy formulation of the Stokes equation using same degree of polynomials for the primal and mixed variables. The novel formulation ...

This work presents a dispersion analysis of the Hybrid Discontinuous Galerkin (HDG) method. Considering the Helmholtz system, we quantify the discrepancies between the exact and discrete wavenumbers. In particular, we obtain an analytic expansion for ...

We derive error estimates for the piecewise linear finite element approximation of the Laplace---Beltrami operator on a bounded, orientable, $$C^3$$C3, surface without boundary on general shape regular meshes. As an application, we consider a problem ...

An H(div) conforming finite element method for solving the linear Biot equations is analyzed. Formulations for the standard mixed method are combined with formulation of interior penalty discontinuous Galerkin method to obtain a consistent scheme. ...

In this paper, we present new upscaled HDG methods for Brinkman equations in the context of high-contrast heterogeneous media. The a priori error estimates are derived in terms of both fine and coarse scale parameters that depend on the high-contrast ...

We further investigate the high order positivity-preserving discontinuous Galerkin (DG) methods for linear hyperbolic and radiative transfer equations developed in Yuan et al. (SIAM J Sci Comput 38:A2987---A3019, 2016). The DG methods in Yuan et al. (...

In this work we present a method for the computation of numerical solutions of 2D homogeneous isotropic elastodynamics equations by solving scalar wave equations. These equations act on the potentials of a Helmholtz decomposition of the displacement ...

We study the $$h$$h- and $$p$$p-versions of non-conforming harmonic virtual element methods (VEM) for the approximation of the Dirichlet---Laplace problem on a 2D polygonal domain, providing quasi-optimal error bounds. Harmonic VEM do not make use of ...

We analyze space semi-discretizations of linear, second-order wave equations by discontinuous Galerkin methods in polygonal domains where solutions exhibit singular behavior near corners. To resolve these singularities, we consider two families of ...

We present optimal preconditioners for a recently introduced hybridized discontinuous Galerkin finite element discretization of the Stokes equations. Typical of hybridized discontinuous Galerkin methods, the method has degrees-of-freedom that can be ...

The NURBS-enhanced finite element method (NEFEM) combined with a hybridisable discontinuous Galerkin (HDG) approach is presented for the first time. The proposed technique completely eliminates the uncertainty induced by a polynomial approximation of ...