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- <meta name="author" content="Wolfgang Bangerth <deal@iwr.uni-heidelberg.de>">
- <meta name="keywords" content="Publications on and with deal.II"></head>
+ <meta name="author" content="Guido Kanschat <deal@iwr.uni-heidelberg.de>">
+ <meta name="keywords" content="deal.II DGFEM discontinuous Galerkin"></head>
<body>
-
+<h1>Superconvergence of the Local Discontinuous Galerkin
+ Method for Elliptic Problems on Cartesian Grids</h1>
+Bernardo Cockburn, <a href="http://gaia.iwr.uni-heidelberg.de/~kanschat"
+ target="_top">Guido Kanschat</a>, Ilaria Perugia, Dominik Schötzau
<h3>Abstract</h3>
<dir>
--- /dev/null
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0//EN"
+ "http://www.w3.org/TR/REC-html40/strict.dtd">
+<html>
+ <head>
+ <link href="../../screen.css" rel="StyleSheet" title="deal.II Homepage" media="screen">
+ <link href="../../print.css" rel="StyleSheet" title="deal.II Homepage" media="print">
+ <title>The deal.II Homepage</title>
+ <meta name="author" content="Wolfgang Bangerth <deal@iwr.uni-heidelberg.de>">
+ <meta name="keywords" content="Publications on and with deal.II"></head>
+ <body>
+ <pre>
+
+@TechReport{CKSS00,
+ author = {Cockburn, Bernardo and Kanschat, Guido and Sch{\"o}tzau, Dominik and Schwab, Christoph},
+ title = {Local discontinuous {G}alerkin methods for the {S}tokes
+ system},
+ institution = IMA,
+ year = 2000,
+ number = 1728,
+ month = {oct},
+ note = {submitted to SIAM J. Numer. Anal.}
+}
+
+</pre></body></html>
--- /dev/null
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0//EN"
+ "http://www.w3.org/TR/REC-html40/strict.dtd">
+<html>
+ <head>
+ <link href="../../screen.css" rel="StyleSheet" title="deal.II Homepage" media="screen">
+ <link href="../../print.css" rel="StyleSheet" title="deal.II Homepage" media="print">
+ <title>The deal.II Homepage</title>
+ <meta name="author" content="Guido Kanschat <deal@iwr.uni-heidelberg.de>">
+ <meta name="keywords" content="deal.II DGFEM discontinuous Galerkin Stokes"></head>
+ <body>
+
+<h1>Local discontinuous Galerkin methods for the Stokes system</h1>
+Bernardo Cockburn,
+ <a href="http://gaia.iwr.uni-heidelberg.de/~kanschat"
+ target="_top">Guido Kanschat</a>, Dominik Schötzau, Christoph Schwab
+<h3>Abstract</h3>
+
+<dir>
+In this paper, we introduce and analyze local discontinuous Galerkin
+methods for the Stokes system. For arbitrary meshes with hanging
+nodes and elements of various shapes we derive a priori estimates for
+the <i>L<sup>2</sup></i>-norm of the errors in the velocities and
+the pressure. We show that <b>optimal</b> order estimates are
+obtained when polynomials of degree <i>k</i> are used for each
+component of the velocity and polynomials of degree <i>k</i>-1 for the
+pressure, for any <i>k</i>>1. We also consider the case in which
+<b>all</b> the unknowns are approximated with polynomials of degree <i>k</i>
+and show that, although the orders of convergence remain the same, the
+method is more efficient. Numerical experiments verifying these facts
+are displayed.
+</dir>
+
+</body>
+</html>
--- /dev/null
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0//EN"
+ "http://www.w3.org/TR/REC-html40/strict.dtd">
+<html>
+ <head>
+ <link href="../../screen.css" rel="StyleSheet" title="deal.II Homepage" media="screen">
+ <link href="../../print.css" rel="StyleSheet" title="deal.II Homepage" media="print">
+ <title>The deal.II Homepage</title>
+ <meta name="author" content="Wolfgang Bangerth <deal@iwr.uni-heidelberg.de>">
+ <meta name="keywords" content="Publications on and with deal.II"></head>
+ <body>
+ <pre>
+
+@TechReport{GK00,
+ author = {Gopalakrishnan, J. and Kanschat, G.},
+ title = {A Multilevel Discontinuous {G}alerkin Method},
+ institution = IMA,
+ year = 2000,
+ type = {Preprint},
+ number = 1735,
+ month = dec
+}
+
+</pre></body></html>
--- /dev/null
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0//EN"
+ "http://www.w3.org/TR/REC-html40/strict.dtd">
+<html>
+ <head>
+ <link href="../../screen.css" rel="StyleSheet" title="deal.II Homepage" media="screen">
+ <link href="../../print.css" rel="StyleSheet" title="deal.II Homepage" media="print">
+ <title>The deal.II Homepage</title>
+ <meta name="author" content="Guido Kanschat <deal@iwr.uni-heidelberg.de>">
+ <meta name="keywords" content="deal.II DGFEM discontinuous Galerkin multigrid"></head>
+ <body>
+
+<h1>A Multilevel Discontinuous Galerkin Method</h1>
+J. Gopalakrishnan,
+ <a href="http://gaia.iwr.uni-heidelberg.de/~kanschat"
+ target="_top">G. Kanschat</a>
+<h3>Abstract</h3>
+
+<dir>
+A variable V-cycle preconditioner for an interior penalty finite
+element discretization for elliptic problems is presented. An analysis
+under a mild regularity assumption shows that the preconditioner is
+uniform. The interior penalty method is then combined with a
+discontinuous Galerkin scheme to arrive at a discretization scheme for
+an advection-diffusion problem, for which an error estimate is
+proved. A multigrid algorithm for this method
+is presented, and numerical experiments indicating its robustness
+with respect to diffusion coefficient are reported.
+</dir>
+
+</body>
+</html>
<h3>Publications in 2000</h3>
<ol>
+ <li> <p>
+ J. Gopalakrishnan,
+ <a href="http://gaia.iwr.uni-heidelberg.de/~kanschat"
+ target="_top">G. Kanschat</a>
+ <br>
+ <strong> A Multilevel Discontinuous Galerkin Method
+ </strong>
+ <br>
+ IMA Preprint 1735, December 2000
+ <br>
+ (<a href="2000/gk.html" target="body">Abstract</a>,
+ <a href="2000/gk.bib" target="body">BibTeX
+ entry</a>,
+ <a href="http://www.ima.umn.edu/preprints/dec2000/1735.ps">Postscript</a>)
+ </p>
+
+ <li> <p>
+ Bernardo Cockburn,
+ <a href="http://gaia.iwr.uni-heidelberg.de/~kanschat"
+ target="_top">Guido Kanschat</a>, Dominik Schötzau, Christoph Schwab
+ <br>
+ <strong> Local discontinuous Galerkin methods for the Stokes
+ system
+ </strong>
+ <br>
+ IMA Preprint 1728, October 2000
+ <br>
+ (<a href="2000/ckss.html" target="body">Abstract</a>,
+ <a href="2000/ckss.bib" target="body">BibTeX
+ entry</a>,
+ <a href="http://www.ima.umn.edu/preprints/oct2000/1728.ps">Postscript</a>)
+ </p>
+
<li> <p>
<a href="http://gaia.iwr.uni-heidelberg.de/~wolf"
target="_top">Wolfgang Bangerth</a>
Method for Elliptic Problems on Cartesian Grids
</strong>
<br>
- Preprint no. 2000/71, University of Minnesota Super Computing Institute
+ IMA Preprint 1695, April 2000
<br>
(<a href="2000/ckps.html" target="body">Abstract</a>,
<a href="2000/ckps.bib" target="body">BibTeX
- entry</a>)
+ entry</a>,
+ <a href="http://www.ima.umn.edu/preprints/apr2000/1695.ps">Postscript</a>)
</p>
</ol>