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 Guido Kanschat

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Average citations per article15.67
Citation Count235
Publication count15
Publication years1997-2017
Available for download1
Average downloads per article1,855.00
Downloads (cumulative)1,855
Downloads (12 Months)181
Downloads (6 Weeks)21
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15 results found Export Results: bibtexendnoteacmrefcsv

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1
January 2017 Journal of Computational and Applied Mathematics: Volume 310 Issue C, January 2017
Publisher: Elsevier Science Publishers B. V.
Bibliometrics:
Citation Count: 0

We apply geometric multigrid methods for the finite element approximation of flow problems governed by Darcy and Brinkman systems used in modeling highly heterogeneous porous media. The method is based on divergence-conforming discontinuous Galerkin methods and overlapping, patch based domain decomposition smoothers. We show in benchmark experiments that the method ...
Keywords: Heterogeneous porous media, Darcy and Brinkman flows, Multigrid methods, Preconditioning

2
April 2010 SIAM Journal on Numerical Analysis: Volume 48 Issue 1, April 2010
Publisher: Society for Industrial and Applied Mathematics
Bibliometrics:
Citation Count: 5

We revisit some results from M. L. Adams [ Nucl. Sci. Engrg. , 137 (2001), pp. 298-333]. Using functional analytic tools we prove that a necessary and sufficient condition for the standard upwind discontinuous Galerkin approximation to converge to the correct limit solution in the diffusive regime is that the ...
Keywords: diffusion limit, discontinuous Galerkin, finite elements, neutron transport

3
April 2010 SIAM Journal on Numerical Analysis: Volume 48 Issue 1, April 2010
Publisher: Society for Industrial and Applied Mathematics
Bibliometrics:
Citation Count: 0

We revisit some results from M. L. Adams [ Nucl. Sci. Engrg. , 137 (2001), pp. 298-333]. Using functional analytic tools we prove that a necessary and sufficient condition for the standard upwind discontinuous Galerkin approximation to converge to the correct limit solution in the diffusive regime is that the ...
Keywords: diffusion limit, discontinuous Galerkin, finite elements, neutron transport

4
July 2009 Journal of Scientific Computing: Volume 40 Issue 1-3, July 2009
Publisher: Plenum Press
Bibliometrics:
Citation Count: 11

We introduce and analyze a discontinuous Galerkin method for the incompressible Navier-Stokes equations that is based on finite element spaces of the same polynomial order for the approximation of the velocity and the pressure. Stability of this equal-order approach is ensured by a pressure stabilization term. A simple element-by-element post-processing ...
Keywords: Equal-order methods, Discontinuous Galerkin methods, Incompressible Navier-Stokes equations

5
December 2008 SIAM Journal on Numerical Analysis: Volume 47 Issue 1, October 2008
Publisher: Society for Industrial and Applied Mathematics
Bibliometrics:
Citation Count: 4

We study the convergence of an adaptive interior penalty discontinuous Galerkin (IPDG) method for a two-dimensional model second order elliptic boundary value problem. Based on a residual-type a posteriori error estimator, we prove that after each refinement step of the adaptive scheme we achieve a guaranteed reduction of the global ...
Keywords: adaptive methods, discontinuous Galerkin, error estimates, interior penalty

6
August 2008 Journal of Computational and Applied Mathematics: Volume 218 Issue 1, August, 2008
Publisher: Elsevier Science Publishers B. V.
Bibliometrics:
Citation Count: 2

The multigrid method for discontinuous Galerkin (DG) discretizations of advection-diffusion problems is presented. It is based on a block Gauss-Seidel smoother with downwind ordering honoring the advection operator. The cell matrices of the DG scheme are inverted in this smoother in order to obtain robustness for higher order elements. Employing ...
Keywords: Discontinuous Galerkin, 65M55, Advection, Multigrid, 74S05, Finite elements, High order

7 published by ACM
August 2007 ACM Transactions on Mathematical Software (TOMS): Volume 33 Issue 4, August 2007
Publisher: ACM
Bibliometrics:
Citation Count: 93
Downloads (6 Weeks): 21,   Downloads (12 Months): 181,   Downloads (Overall): 1,855

Full text available: PDFPDF
An overview of the software design and data abstraction decisions chosen for deal.II, a general purpose finite element library written in C++, is given. The library uses advanced object-oriented and data encapsulation techniques to break finite element implementations into smaller blocks that can be arranged to fit users requirements. Through ...
Keywords: Object-orientation, software design

8
May 2007 Journal of Scientific Computing: Volume 31 Issue 1-2, May 2007
Publisher: Plenum Press
Bibliometrics:
Citation Count: 20

We present a class of discontinuous Galerkin methods for the incompressible Navier---Stokes equations yielding exactly divergence-free solutions. Exact incompressibility is achieved by using divergence-conforming velocity spaces for the approximation of the velocities. The resulting methods are locally conservative, energy-stable, and optimally convergent. We present a set of numerical tests that ...
Keywords: discontinuous Galerkin methods, divergence-free condition, Navier---Stokes equations

9
June 2005 Journal of Scientific Computing: Volume 22-23 Issue 1, June 2005
Publisher: Plenum Press
Bibliometrics:
Citation Count: 2

We present a block preconditioner for LDG discretizations of Stokes equations. The dependence of its performance on the discretization parameters is investigated. An extension to Oseen equations is shown, yielding efficient and robust solvers in a wide regime of Reynolds numbers.
Keywords: Oseen equations, preconditioners, saddle-point problems, Stokes equations, discontinuous Galerkin, finite elements

10
September 2003 Numerische Mathematik: Volume 95 Issue 3, September 2003
Publisher: Springer-Verlag New York, Inc.
Bibliometrics:
Citation Count: 6

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 ...

11
September 2003 Numerische Mathematik: Volume 95 Issue 3, September 2003
Publisher: Springer-Verlag New York, Inc.
Bibliometrics:
Citation Count: 0


12
March 2003 SIAM Journal on Scientific Computing: Volume 25 Issue 3, 2003
Publisher: Society for Industrial and Applied Mathematics
Bibliometrics:
Citation Count: 4

A multilevel interior penalty method is used as an efficient preconditioner for the Schur complement of the local discontinuous Galerkin (LDG) discretization of a Poisson problem. The method is then used in a block-triangular preconditioner of the LDG saddle point system. The block preconditioner is of the same efficiency as ...
Keywords: finite elements, saddle point problem, multigrid, local discontinuous Galerkin, preconditioning

13
January 2002 SIAM Journal on Numerical Analysis: Volume 40 Issue 1, 2002
Publisher: Society for Industrial and Applied Mathematics
Bibliometrics:
Citation Count: 44

In this paper, we introduce and analyze local discontinuous Galerkin methods for the Stokes system. For a class of shape regular meshes with hanging nodes we derive a priori estimates for the L 2 -norm of the errors in the velocities and the pressure. We show that optimal -order estimates ...
Keywords: finite elements, discontinuous Galerkin methods, Stokes system

14
January 2001 SIAM Journal on Numerical Analysis: Volume 39 Issue 1, 2001
Publisher: Society for Industrial and Applied Mathematics
Bibliometrics:
Citation Count: 41

In this paper, we present a superconvergence result for the local discontinuous Galerkin (LDG) method for a model elliptic problem on Cartesian grids. We identify a special numerical flux for which the L 2 -norm of the gradient and the L 2 -norm of the potential are of orders k ...
Keywords: superconvergence, Cartesian grids, elliptic problems, finite elements, discontinuous Galerkin methods

15
August 1997 Computing: Volume 58 Issue 4, 1997
Publisher: Springer-Verlag New York, Inc.
Bibliometrics:
Citation Count: 2

Keywords: finite element methods, a posteriori error estimates, neutron transport, radiative transfer, Boltzmann equation



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