From: Guido Kanschat Date: Tue, 9 Jan 2001 14:28:13 +0000 (+0000) Subject: IMA preprints 1728 & 1735 X-Git-Tag: v8.0.0~19841 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=597b4bcff7bbb0cd16553e7b75074eabf44eaa18;p=dealii.git IMA preprints 1728 & 1735 git-svn-id: https://svn.dealii.org/trunk@3622 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/doc/publications/2000/ckps.html b/deal.II/doc/publications/2000/ckps.html index 55f1f32ecc..1930dee948 100644 --- a/deal.II/doc/publications/2000/ckps.html +++ b/deal.II/doc/publications/2000/ckps.html @@ -5,11 +5,14 @@ The deal.II Homepage - - + + - +

Superconvergence of the Local Discontinuous Galerkin + Method for Elliptic Problems on Cartesian Grids

+Bernardo Cockburn, Guido Kanschat, Ilaria Perugia, Dominik Schötzau

Abstract

diff --git a/deal.II/doc/publications/2000/ckss.bib b/deal.II/doc/publications/2000/ckss.bib new file mode 100644 index 0000000000..9ebf72af48 --- /dev/null +++ b/deal.II/doc/publications/2000/ckss.bib @@ -0,0 +1,24 @@ + + + + + + The deal.II Homepage + + + + 
+
+@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.}
+}
+
+
diff --git a/deal.II/doc/publications/2000/ckss.html b/deal.II/doc/publications/2000/ckss.html new file mode 100644 index 0000000000..eeb8b1a027 --- /dev/null +++ b/deal.II/doc/publications/2000/ckss.html @@ -0,0 +1,34 @@ + + + + + + The deal.II Homepage + + + + +

Local discontinuous Galerkin methods for the Stokes system

+Bernardo Cockburn, + Guido Kanschat, Dominik Schötzau, Christoph Schwab +

Abstract

+ + +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 L2-norm of the errors in the velocities and +the pressure. We show that optimal order estimates are +obtained when polynomials of degree k are used for each +component of the velocity and polynomials of degree k-1 for the +pressure, for any k>1. We also consider the case in which +all the unknowns are approximated with polynomials of degree k +and show that, although the orders of convergence remain the same, the +method is more efficient. Numerical experiments verifying these facts +are displayed. + + + + diff --git a/deal.II/doc/publications/2000/gk.bib b/deal.II/doc/publications/2000/gk.bib new file mode 100644 index 0000000000..bf33c024a7 --- /dev/null +++ b/deal.II/doc/publications/2000/gk.bib @@ -0,0 +1,23 @@ + + + + + + The deal.II Homepage + + + + 
+
+@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
+}
+
+
diff --git a/deal.II/doc/publications/2000/gk.html b/deal.II/doc/publications/2000/gk.html new file mode 100644 index 0000000000..37455d4f8c --- /dev/null +++ b/deal.II/doc/publications/2000/gk.html @@ -0,0 +1,31 @@ + + + + + + The deal.II Homepage + + + + +

A Multilevel Discontinuous Galerkin Method

+J. Gopalakrishnan, + G. Kanschat +

Abstract

+ + +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. + + + + diff --git a/deal.II/doc/publications/toc.html b/deal.II/doc/publications/toc.html index 990f9c5926..ed5f1cf165 100644 --- a/deal.II/doc/publications/toc.html +++ b/deal.II/doc/publications/toc.html @@ -41,6 +41,39 @@

Publications in 2000

    +

  1. + J. Gopalakrishnan, + G. Kanschat +
    + A Multilevel Discontinuous Galerkin Method + +
    + IMA Preprint 1735, December 2000 +
    + (Abstract, + BibTeX + entry, + Postscript) +

    + +

  2. + Bernardo Cockburn, + Guido Kanschat, Dominik Schötzau, Christoph Schwab +
    + Local discontinuous Galerkin methods for the Stokes + system + +
    + IMA Preprint 1728, October 2000 +
    + (Abstract, + BibTeX + entry, + Postscript) +

    +

  3. Wolfgang Bangerth @@ -112,11 +145,12 @@ Method for Elliptic Problems on Cartesian Grids
    - Preprint no. 2000/71, University of Minnesota Super Computing Institute + IMA Preprint 1695, April 2000
    (Abstract, BibTeX - entry) + entry, + Postscript)