American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Predicting changes in dynamical behaviour in solutions to stochastic delay differential equations
  • CPAA Home
  • This Issue
  • Next Article
    Extrapolation expansions for Hanging-Chad-Type Galerkin integrals with plane triangular elements
June  2006, 5(2): 349-365. doi: 10.3934/cpaa.2006.5.349

Abstract cascading multigrid preconditioners in Besov spaces

Hermann Brunner 1, and  Jingtang Ma 2,

1. 

Dept. of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL, Canada A1C 5S7
2. 

Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing 100080, China

Received  April 2005 Revised  August 2005 Published  March 2006

In this paper we describe and analyze the general framework of cascading multigrid preconditioning. In particular, we introduce two preconditioners based on the cascading multigrid approach. We then illustrate the application of the corresponding method to the heat equation with mild regularity in Besov spaces. Furthermore, we analyze a cascading multigrid preconditioner for the interior penalty discontinuous Galerkin method.
Keywords: discontinuous Galerkin method., Cascading multigrid method, preconditioner, finite element method, Besov spaces.
Mathematics Subject Classification: 65F10, 65N55, 65N30, 65R2.
Citation: Hermann Brunner, Jingtang Ma. Abstract cascading multigrid preconditioners in Besov spaces. Communications on Pure & Applied Analysis, 2006, 5 (2) : 349-365. doi: 10.3934/cpaa.2006.5.349
[1]

Runchang Lin, Huiqing Zhu. A discontinuous Galerkin least-squares finite element method for solving Fisher's equation. Conference Publications, 2013, 2013 (special) : 489-497. doi: 10.3934/proc.2013.2013.489
[2]

Chaoxu Pei, Mark Sussman, M. Yousuff Hussaini. A space-time discontinuous Galerkin spectral element method for the Stefan problem. Discrete & Continuous Dynamical Systems - B, 2018, 23 (9) : 3595-3622. doi: 10.3934/dcdsb.2017216
[3]

Yoshifumi Aimoto, Takayasu Matsuo, Yuto Miyatake. A local discontinuous Galerkin method based on variational structure. Discrete & Continuous Dynamical Systems - S, 2015, 8 (5) : 817-832. doi: 10.3934/dcdss.2015.8.817
[4]

Xin-Guo Liu, Kun Wang. A multigrid method for the maximal correlation problem. Numerical Algebra, Control & Optimization, 2012, 2 (4) : 785-796. doi: 10.3934/naco.2012.2.785
[5]

Cornel M. Murea, H. G. E. Hentschel. A finite element method for growth in biological development. Mathematical Biosciences & Engineering, 2007, 4 (2) : 339-353. doi: 10.3934/mbe.2007.4.339
[6]

Martin Burger, José A. Carrillo, Marie-Therese Wolfram. A mixed finite element method for nonlinear diffusion equations. Kinetic & Related Models, 2010, 3 (1) : 59-83. doi: 10.3934/krm.2010.3.59
[7]

Armando Majorana. A numerical model of the Boltzmann equation related to the discontinuous Galerkin method. Kinetic & Related Models, 2011, 4 (1) : 139-151. doi: 10.3934/krm.2011.4.139
[8]

Binjie Li, Xiaoping Xie, Shiquan Zhang. New convergence analysis for assumed stress hybrid quadrilateral finite element method. Discrete & Continuous Dynamical Systems - B, 2017, 22 (7) : 2831-2856. doi: 10.3934/dcdsb.2017153
[9]

Kun Wang, Yinnian He, Yueqiang Shang. Fully discrete finite element method for the viscoelastic fluid motion equations. Discrete & Continuous Dynamical Systems - B, 2010, 13 (3) : 665-684. doi: 10.3934/dcdsb.2010.13.665
[10]

Junjiang Lai, Jianguo Huang. A finite element method for vibration analysis of elastic plate-plate structures. Discrete & Continuous Dynamical Systems - B, 2009, 11 (2) : 387-419. doi: 10.3934/dcdsb.2009.11.387
[11]

So-Hsiang Chou. An immersed linear finite element method with interface flux capturing recovery. Discrete & Continuous Dynamical Systems - B, 2012, 17 (7) : 2343-2357. doi: 10.3934/dcdsb.2012.17.2343
[12]

Donald L. Brown, Vasilena Taralova. A multiscale finite element method for Neumann problems in porous microstructures. Discrete & Continuous Dynamical Systems - S, 2016, 9 (5) : 1299-1326. doi: 10.3934/dcdss.2016052
[13]

Qingping Deng. A nonoverlapping domain decomposition method for nonconforming finite element problems. Communications on Pure & Applied Analysis, 2003, 2 (3) : 297-310. doi: 10.3934/cpaa.2003.2.297
[14]

Runchang Lin. A robust finite element method for singularly perturbed convection-diffusion problems. Conference Publications, 2009, 2009 (Special) : 496-505. doi: 10.3934/proc.2009.2009.496
[15]

Kim S. Bey, Peter Z. Daffer, Hideaki Kaneko, Puntip Toghaw. Error analysis of the p-version discontinuous Galerkin method for heat transfer in built-up structures. Communications on Pure & Applied Analysis, 2007, 6 (3) : 719-740. doi: 10.3934/cpaa.2007.6.719
[16]

Xia Ji, Wei Cai. Accurate simulations of 2-D phase shift masks with a generalized discontinuous Galerkin (GDG) method. Discrete & Continuous Dynamical Systems - B, 2011, 15 (2) : 401-415. doi: 10.3934/dcdsb.2011.15.401
[17]

Mahboub Baccouch. Superconvergence of the semi-discrete local discontinuous Galerkin method for nonlinear KdV-type problems. Discrete & Continuous Dynamical Systems - B, 2019, 24 (1) : 19-54. doi: 10.3934/dcdsb.2018104
[18]

Zheng Sun, José A. Carrillo, Chi-Wang Shu. An entropy stable high-order discontinuous Galerkin method for cross-diffusion gradient flow systems. Kinetic & Related Models, 2019, 12 (4) : 885-908. doi: 10.3934/krm.2019033
[19]

Na An, Chaobao Huang, Xijun Yu. Error analysis of discontinuous Galerkin method for the time fractional KdV equation with weak singularity solution. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 0-0. doi: 10.3934/dcdsb.2019185
[20]

Caterina Calgaro, Meriem Ezzoug, Ezzeddine Zahrouni. Stability and convergence of an hybrid finite volume-finite element method for a multiphasic incompressible fluid model. Communications on Pure & Applied Analysis, 2018, 17 (2) : 429-448. doi: 10.3934/cpaa.2018024

2018 Impact Factor: 0.925

Tools

Metrics

  • PDF downloads (8)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences