A Scalable Preconditioner for a Primal Discontinuous Petrov--Galerkin Method

A Relation between the Discontinuous Petrov--Galerkin Method and the Discontinuous Galerkin Method

This paper is an attempt in seeking a connection between the discontinuous Petrov– Galerkin method of Demkowicz and Gopalakrishnan [13,15] and the popular discontinuous Galerkin method. Starting from a discontinuous Petrov–Galerkin (DPG) method with zero enriched order we re-derive a large class of discontinuous Galerkin (DG) methods for first order hyperbolic and elliptic equations. The first ...

A Multilevel Preconditioner for the Interior Penalty Discontinuous Galerkin Method

In this article we present a multilevel preconditioner for interior penalty discontinuous Galerkin discretizations of second order elliptic boundary value problems that gives rise to uniformly bounded condition numbers without any additional regularity assumptions on the solution. The underlying triangulations are only assumed to be shape regular but may have hanging nodes subject to certain mi...

A hybridized discontinuous Petrov–Galerkin scheme for scalar conservation laws

We present a hybridized discontinuous Petrov–Galerkin (HDPG) method for the numerical solution of steady and time-dependent scalar conservation laws. The method combines a hybridization technique with a local Petrov–Galerkin approach in which the test functions are computed to maximize the inf-sup condition. Since the Petrov–Galerkin approach does not guarantee a conservative solution, we propo...

A Discontinuous Petrov-Galerkin Methodology for Incompressible Flow Problems

Discontinuous Petrov Galerkin Method (dpg) with Optimal Test Functions. a Finite Element Method for All Seasons?

ה ןויעה םוי 35 חשיא לש " מ 0 1 רבוטקואב 013 2 , ןב תטיסרבינוא ןוירוג , ראב עבש , לארשי