L. Donatella Marini

Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems

We provide a framework for the analysis of a large class of discontinuous methods for second-order elliptic problems. It allows for the understanding and comparison of most of the discontinuous Galerkin methods that have been proposed over the past three decades for the numerical treatment of elliptic problems.

Residual-free bubbles for advection-diffusion problems: the general error analysis

Summary. We develop the general a priori error analysis of residual-free bubble finite element approximations to non-self-adjoint elliptic problems of the form

Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems

(\varepsilon A + C)u = f

A Family of Discontinuous Galerkin Finite Elements for the Reissner--Mindlin Plate

subject to homogeneous Dirichlet boundary condition, where A is a symmetric second-order elliptic operator, C is a skew-symmetric first-order differential operator, and

MIXED FINITE ELEMENT METHODS WITH CONTINUOUS STRESSES

\varepsilon

Error estimates for the three-field formulation with bubble stabilization

is a positive parameter. Optimal-order error bounds are derived in various norms, using piecewise polynomial finite elements of degree

A Simple Preconditioner for a Discontinuous Galerkin Method for the Stokes Problem

k\geq 1

A-Posteriori Error Estimates for Discontinuous Galerkin Approximations of Second Order Elliptic Problems

.

H(div) and H(curl)-conforming virtual element methods.

We apply the weighted-residual approach recently introduced in [F. Brezzi et al., Comput. Methods Appl. Mech. Engrg., 195 (2006), pp. 3293-3310] to derive discontinuous Galerkin formulations for advection-diffusion-reaction problems. We devise the basic ingredients to ensure stability and optimal error estimates in suitable norms, and propose two new methods.

Virtual Element Method for fourth order problems: L-2-estimates

We develop a family of locking-free elements for the Reissner–Mindlin plate using Discontinuous Galerkin (DG) techniques, one for each odd degree, and prove optimal error estimates. A second family uses conforming elements for the rotations and nonconforming elements for the transverse displacement, generalizing the element of Arnold and Falk to higher degree.