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A Variational Multiscale Method for Poisson’s Equation in Mixed Form

In: Numerical Mathematics and Advanced Applications 2011

Author

Listed:
  • M. G. Larson

    (Umeå University, Department of Mathematics)

  • A. Målqvist

    (Uppsala University, Department of Information Technology)

  • R. Söderlund

    (Umeå University, Department of Mathematics)

Abstract

In this paper we present the adaptive variational multiscale method for solving the Poisson equation in mixed form. We use the method introduced in Larson and Målqvist (Comput Method Appl Mech Eng 196:2313–2324, 2007), and further analyzed and applied to mixed problems in Larson and Målqvist (Comput Method Appl Mech Eng 19:1017–1042, 2009), which is a general tool for solving linear partial differential equations with multiscale features in the coefficients. We extend the numerics in Larson and Målqvist (Comput Method Appl Mech Eng 19:1017–1042, 2009) from rectangular meshes to triangular meshes which allow for computation on more complicated domains. A new a posteriori error estimate is also included, which is used in an adaptive algorithm. We present a numerical example that shows the efficiency of incorporating a posteriori based adaptivity into the method.

Suggested Citation

  • M. G. Larson & A. Målqvist & R. Söderlund, 2013. "A Variational Multiscale Method for Poisson’s Equation in Mixed Form," Springer Books, in: Andrea Cangiani & Ruslan L. Davidchack & Emmanuil Georgoulis & Alexander N. Gorban & Jeremy Levesley (ed.), Numerical Mathematics and Advanced Applications 2011, edition 127, pages 713-721, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-33134-3_75
    DOI: 10.1007/978-3-642-33134-3_75
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