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Implementation of the Mortar Method in the Wavelet Context

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Abstract

The paper is concerned with non-conforming wavelet-type discretization of elliptic partial differential equations. In particular it analyzes some implementation issues related to the form of the constraint operator in the Mortar approach. Moreover it gives a preliminary example of the coupling of wavelets with finite elements in non-trivial geometries.

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References

  • Abdoulaev G., Achdou Y., Kutznetsov Y., Prud’homme C (1999). On the parallel inplementation of the mortar element method M2AN Math. Model. Numer. Anal. 33(2): 245–259

    Article  MATH  MathSciNet  Google Scholar 

  • Achdou Y., Pironneau O. (1993). A fast solver for Navier–Stokes equations in the laminar regime using mortar finite element and boundary element method. SIAM J. Numer. Anal. 32(4): 985–1016

    Article  MathSciNet  Google Scholar 

  • Anagnostou, G., Maday, Y., and Patera, A. T. (1991) A sliding mesh method for partial differential equations in nonstationary geometries: application to the incompressible Navier–Stokes equations Technical Report 91024, Laboratoire d’Analyse Numérique

  • Anderson L., Hall N., Jawerth B., Peters G. (1993) Wavelets on closed subsets on the real line. In: Schumaker L.L., Webb G. (ed). Topics in the Theory and Applications of Wavelets, 1993. Academic Press, Boston MA, pp. 1–61

    Google Scholar 

  • Ben Belgacem F. (1999). The mortar element method with Lagrange multiplier. Numer. Math. 84(2): 173–197

    Article  MATH  MathSciNet  Google Scholar 

  • Ben Belgacem F., Buffa A., Maday Y. (2001). The mortar element method for 3d Maxwell’s equations: First results. SIAM J. Numer. Anal. 39(3): 880–901

    Article  MATH  MathSciNet  Google Scholar 

  • Belhachmi, Z., and Bernardi, C. (1994). The mortar spectral element method for fourth-order problems. Comp. Meth. Appl Mech. Eng., 116

  • Bertoluzza, S. (1997). An adaptive wavelet collocation method based on interpolating wavelets. In Multiscale Wavelet Methods for Partial Differential Equations, vol. 6 of Wavelets Analysis and its Applications, pages 109–135. Academic Press, pp. 109–133

  • Bertoluzza, S., Falletta, S., and Perrier, V. (2002). Wavelet/fem coupling by the mortar method. In Lecture Notes in Computational Science and Engineering, pp. 119–132

  • Bertoluzza S., Mazet S., Verani M. (2002). A nonlinear Richardson algorithm for the solution of elliptic PDE’s Math. Models Meth. Appl. Sci. 2, 143–158

    Google Scholar 

  • Bertoluzza S., Perrier V. (2001). The mortar method in the wavelet context. ESAIM:M2AN. 4, 647–673

    Article  MATH  MathSciNet  Google Scholar 

  • Bertoluzza S., Pietra P. (2000). Space frequency adaptive approximation for quantum hydrodynamic models. Transport Theory Stat. Phys. 28, 375–395

    Google Scholar 

  • Canuto C., Tabacco A., Urban K. (2000). The wavelet element method. II. Realization and additional features in 2D and 3D. Appl. Comput. Harmon. Anal. 8(2): 123–165

    Article  MATH  MathSciNet  Google Scholar 

  • Charton P., Perrier V. (1996). A pseudo-wavelet scheme for the two-dimensional Navier-Stokes equation. Comp. Appl Math. 15, 139–160

    MATH  MathSciNet  Google Scholar 

  • Cohen A. (2000). Numerical analysis of wavelet methods. In: Ciarlet P.G., Lions J.L. (ed). Handbook in Numerical Analysis, vol. VII. Elsevier Science Publishers, North Holland

    Google Scholar 

  • Cohen A., Daubechies I., Vial P. (1993). Wavelets on the interval and fast wavelet transforms. ACHA, 1, 54–81

    MATH  MathSciNet  Google Scholar 

  • Cohen A., Masson R. (2000). Wavelet adaptive method for second order elliptic problems: boundary conditions and domain decomposition. Numer. Math. 86(2): 193–238

    Article  MATH  MathSciNet  Google Scholar 

  • Dahlke S., Dahmen W., Hochmut R., Schneider R. (1997) Stable multiscale bases and local error estimation for elliptic problems. Appl. Numer. Math. 23, 21–48

    Article  MATH  MathSciNet  Google Scholar 

  • Dahmen W., Kunoth A. (1992). Multilevel preconditioning Numer. Math. 63, 315–344

    Article  MATH  MathSciNet  Google Scholar 

  • Dahmen W., Kunoth A., Urban K. (1999). Biorthogonal spline-wavelets on the interval – stability and moment condition. ACHA 6, 132–196

    MATH  MathSciNet  Google Scholar 

  • Dahmen W., Schneider R. (1998). Wavelets with complementary boundary conditions – Function spaces on the cube. Results Math. 34, 255–293

    MATH  MathSciNet  Google Scholar 

  • Dahmen W., Schneider R. (1999). Wavelets on manifolds. I Construction and domain decomposition. SIAM J. Math Anal. 31(1): 184–230

    Article  MATH  MathSciNet  Google Scholar 

  • Daubechies, I. (1992). Ten lectures on wavelets In CBMS Lecture Notes, vol. 61. SIAM, Philadelphia

  • Jaffard S. (1992). Wavelet methods for fast resolution of elliptic problems. SIAM J. Numer. Anal 29, 965–986

    Article  MATH  MathSciNet  Google Scholar 

  • Maday, Y., Perrier, V., and Ravel, J.C. (1991). Adaptivité dynamique sur bases d’ondelettes pour l’approximation d’équations aux derivées partielles. C. R. Acad. Sci Paris, 312(Série I), 405–410

  • Masson, R. (1996). Biorthogonal spline wavelets on the interval for the resolution of boundary problems. M 3 AS 6(6)

  • Meyer, Y. (1990). Ondelettes et Opérateurs. Hermann

  • Monasse P., Perrier V. (1998). Orthonormal wavelet bases adapted for partial differential equations with boundary conditions. SIAM J. Math. Anal. 29, 1040–1065

    Article  MATH  MathSciNet  Google Scholar 

  • Prud’homme, C. (1998). A strategy for the resolution of the tridimensionnal incompressible Navier–Stokes equations. In Méthodes Itératives de Décomposition de Domaines et Communications en Calcul Parallèle, vol. 10 of Calculateurs Parallèles Réséaux et Systèmes Répartis, Hermes pp. 371–380

  • Wohlmuth B. (2000). A mortar finite element method using dual spaces for the Lagrange multiplier. SIAM J. Numer. Anal. 38, 989–1012

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Silvia Falletta.

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Bertoluzza, S., Falletta, S. & Perrier, V. Implementation of the Mortar Method in the Wavelet Context. J Sci Comput 29, 219–255 (2006). https://doi.org/10.1007/s10915-005-9002-7

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  • DOI: https://doi.org/10.1007/s10915-005-9002-7

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