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An Adaptive MFD Method for the Obstacle Problem Read chapter Read first chapter

2013 | OriginalPaper | Chapter

hp–Adaptive Two-Grid Discontinuous Galerkin Finite Element Methods for Quasi-Newtonian Fluid Flows

Authors : S. Congreve, P. Houston, T. P. Wihler

Published in: Numerical Mathematics and Advanced Applications 2011

Publisher: Springer Berlin Heidelberg

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Abstract

We develop the a posteriori error analysis, with respect to a mesh–dependent energy norm, of two-grid hp–version discontinuous Galerkin finite element methods for quasi-Newtonian flows. The performance of the proposed estimators within an hp–adaptive refinement procedure is studied through a numerical experiment.

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previous chapter Application of hp–Adaptive Discontinuous Galerkin Methods to Bifurcation Phenomena in Pipe Flows
next chapter Discontinuous Galerkin Methods for Eigenvalue Problems on Anisotropic Meshes
Literature
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S. Berrone and E. Süli. Two-sided a posteriori error bounds for incompressible quasi-Newtonian flows. IMA J. Numer. Anal., 28:382–421, 2008.MathSciNetMATHCrossRef
2.
C. Bi and V. Ginting. Two-grid discontinuous Galerkin method for quasi-linear elliptic problems. J. Sci. Comput., 49(3):311–331, 2011.MathSciNetMATHCrossRef
3.
S. Congreve, P. Houston, E. Süli, and T. P. Wihler. Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows.
4.
S. Congreve, P. Houston, E. Süli, and T. P. Wihler. Two-grid hp-version discontinuous Galerkin finite element methods for quasi-Newtonian flows. (In preparation).
5.
S. Congreve, P. Houston, and T. P. Wihler. Two-grid hp-version discontinuous Galerkin finite element methods for second-order quasilinear elliptic PDEs. J. Sci. Comput. (in press)
6.
P. Houston and E. Süli. A note on the design of hp-adaptive finite element methods for elliptic partial differential equations. Comput. Methods Appl. Mech. Engrg., 194(2–5):229–243, 2005.MathSciNetMATHCrossRef
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C. Ortner and E Süli. Discontinuous Galerkin finite element approximation of nonlinear second-order elliptic and hyperbolic systems. SIAM J. Numer. Anal., 45(4):1370–1397, 2007.
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Metadata
Title
hp–Adaptive Two-Grid Discontinuous Galerkin Finite Element Methods for Quasi-Newtonian Fluid Flows
Authors
S. Congreve
P. Houston
T. P. Wihler
Copyright Year
2013
Publisher
Springer Berlin Heidelberg
Book
Numerical Mathematics and Advanced Applications 2011

Print ISBN: 978-3-642-33133-6

Electronic ISBN: 978-3-642-33134-3

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-3-642-33134-3_37

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