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L P-Posteriori Error Analysis of Mixed Methods for Linear and Quasilinear Elliptic Problems

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Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 75))

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Abstract

We consider mixed finite element methods for the approximation of linear and quasilinear second-order elliptic problems. A class of postprocessing methods for improving mixed finite element solutions is analyzed. In particular, error estimates in L p, 1 ≤ p ≤ ∞, are given. These postprocessing methods are applicable to all the existing mixed methods, and can be easily implemented. Furthermore, they are local and thus fully parallelizable.

Supported in part by the Army Research Office contract number DAAL03-89-C-0038 with the University of Minnesota Army High Performance Computing Research Center.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Institute for Scientific Computation, Texas A&M University, College Station, TX, 77843, USA

    Zhangxin Chen

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  1. Zhangxin Chen
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Editor information

Editors and Affiliations

  1. Institute for Physical Science and Technology, University of Maryland, 20742, College park, MD, USA

    Ivo Babuska

  2. CIC-3 MS K987 Los Alamos National Laboratory, 87545, Los Alamos, NM, USA

    William D. Henshaw

  3. Research Institute for Advanced Computer Science, NASA Ames Research Center, Mail Stop T20G-5, 94035, Moffet Field, CA, USA

    Joseph E. Oliger

  4. Department of Science and Scientific Computation Research Ctr, Rensselaer Polytechnic Institute, 110-8th St, 12180, Troy, NY, USA

    Joseph E. Flaherty

  5. College of Engineering, Joseph Silbert Dean of Engineering Cornell University Cornell University, 242 Carpenter Hall, 14853, Ithaca, NY, USA

    John E. Hopcroft

  6. Army High Performance Computing Research Center, 1100 South Washington Ave. Suite 101, 55415, Minneapolis, MN, USA

    Tayfun Tezduyar

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© 1995 Springer-Verlag New York

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Chen, Z. (1995). L P-Posteriori Error Analysis of Mixed Methods for Linear and Quasilinear Elliptic Problems. In: Babuska, I., Henshaw, W.D., Oliger, J.E., Flaherty, J.E., Hopcroft, J.E., Tezduyar, T. (eds) Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations. The IMA Volumes in Mathematics and its Applications, vol 75. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4248-2_10

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  • DOI: https://doi.org/10.1007/978-1-4612-4248-2_10

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-8707-0

  • Online ISBN: 978-1-4612-4248-2

  • eBook Packages: Springer Book Archive

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