]> https://gitweb.dealii.org/ - dealii.git/commitdiff
IMA preprints 1728 & 1735
authorGuido Kanschat <dr.guido.kanschat@gmail.com>
Tue, 9 Jan 2001 14:28:13 +0000 (14:28 +0000)
committerGuido Kanschat <dr.guido.kanschat@gmail.com>
Tue, 9 Jan 2001 14:28:13 +0000 (14:28 +0000)
git-svn-id: https://svn.dealii.org/trunk@3622 0785d39b-7218-0410-832d-ea1e28bc413d

deal.II/doc/publications/2000/ckps.html
deal.II/doc/publications/2000/ckss.bib [new file with mode: 0644]
deal.II/doc/publications/2000/ckss.html [new file with mode: 0644]
deal.II/doc/publications/2000/gk.bib [new file with mode: 0644]
deal.II/doc/publications/2000/gk.html [new file with mode: 0644]
deal.II/doc/publications/toc.html

index 55f1f32ecc824fd8db1f7be539426f6bbe69efeb..1930dee94800f1f52aa0891eca99b9b8ecbca013 100644 (file)
@@ -5,11 +5,14 @@
     <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>
+    <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 Sch&ouml;tzau
 <h3>Abstract</h3>
 
 <dir>
diff --git a/deal.II/doc/publications/2000/ckss.bib b/deal.II/doc/publications/2000/ckss.bib
new file mode 100644 (file)
index 0000000..9ebf72a
--- /dev/null
@@ -0,0 +1,24 @@
+<!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>
diff --git a/deal.II/doc/publications/2000/ckss.html b/deal.II/doc/publications/2000/ckss.html
new file mode 100644 (file)
index 0000000..eeb8b1a
--- /dev/null
@@ -0,0 +1,34 @@
+<!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 Sch&ouml;tzau, 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>&gt;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>
diff --git a/deal.II/doc/publications/2000/gk.bib b/deal.II/doc/publications/2000/gk.bib
new file mode 100644 (file)
index 0000000..bf33c02
--- /dev/null
@@ -0,0 +1,23 @@
+<!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>
diff --git a/deal.II/doc/publications/2000/gk.html b/deal.II/doc/publications/2000/gk.html
new file mode 100644 (file)
index 0000000..37455d4
--- /dev/null
@@ -0,0 +1,31 @@
+<!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>
index 990f9c5926e624cae17ada257322c7f44e16fc78..ed5f1cf165fe3e71728500b7dc8196f7c0605576 100644 (file)
     <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 Sch&ouml;tzau, 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>
 

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