A two-grid characteristic finite volume element method for semilinear advection-dominated diffusion equations

Authors

  • Chuanjun Chen,

    Corresponding author
    1. Department of Mathematics and Information Science, Yantai University, Yantai 264005, People's Republic of China
    • Department of Mathematics and Information Science, Yantai University, Yantai 264005, People's Republic of China
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  • Wei Liu,

    1. School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014, People's Republic of China
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  • Chunjia Bi

    1. Department of Mathematics and Information Science, Yantai University, Yantai 264005, People's Republic of China
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Abstract

A two-grid finite volume element method, combined with the modified method of characteristics, is presented and analyzed for semilinear time-dependent advection-dominated diffusion equations in two space dimensions. The solution of a nonlinear system on the fine-grid space (with grid size h) is reduced to the solution of two small (one linear and one nonlinear) systems on the coarse-grid space (with grid size H) and a linear system on the fine-grid space. An optimal error estimate in H1 -norm is obtained for the two-grid method. It shows that the two-grid method achieves asymptotically optimal approximation, as long as the mesh sizes satisfy h = O(H2). Numerical example is presented to validate the usefulness and efficiency of the method. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013

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