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A fully discrete H 1-Galerkin method with quadrature for nonlinear advection–diffusion–reaction equations

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Abstract

We propose and analyze a fully discrete H 1-Galerkin method with quadrature for nonlinear parabolic advection–diffusion–reaction equations that requires only linear algebraic solvers. Our scheme applied to the special case heat equation is a fully discrete quadrature version of the least-squares method. We prove second order convergence in time and optimal H 1 convergence in space for the computer implementable method. The results of numerical computations demonstrate optimal order convergence of scheme in H k for k = 0, 1, 2.

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Authors and Affiliations

  1. Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, CO, 80401, USA

    M. Ganesh

  2. Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dharhan, 31261, Saudi Arabia

    K. Mustapha

Authors
  1. M. Ganesh
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  2. K. Mustapha
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Correspondence to M. Ganesh.

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Support of the Australian Research Council is gratefully acknowledged.

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Ganesh, M., Mustapha, K. A fully discrete H 1-Galerkin method with quadrature for nonlinear advection–diffusion–reaction equations. Numer Algor 43, 355–383 (2006). https://doi.org/10.1007/s11075-007-9066-6

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  • DOI: https://doi.org/10.1007/s11075-007-9066-6

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