Difference schemes for quasi-linear parabolic equations with mixed derivatives-Reference-Cited by-同舟云学术

Difference schemes for quasi-linear parabolic equations with mixed derivatives

Published:2019-06-28 Issue:3 Volume:63 Page:263-269
ISSN:2524-2431
Container-title:Doklady of the National Academy of Sciences of Belarus
language:
Short-container-title:Dokl. Akad. nauk

Author:

Matus P. P.¹,Hieu Le Minh²,Pylak D.³

Affiliation:

1. Institute of Mathematics of the National Academy of Sciences of Belarus; Institute of Mathematics and Computer Science The John Paul II Catholic University of Lublin

2. University of Economics, University of Danang

3. Institute of Mathematics and Computer Science The John Paul II Catholic University of Lublin

Abstract

The present paper is devoted to constructing second-order monotone difference schemes for two-dimensional quasi-linear parabolic equation with mixed derivatives. Two-sided estimates of the solution of specific difference schemes for the original problem are obtained, which are fully consistent with similar estimates of the solution of the differential problem, and the a priori estimate in the uniform norm of C is proved. The estimates obtained are used to prove the convergence of difference schemes in the grid norm of L2.

Publisher

Publishing House Belorusskaya Nauka

Reference12 articles.

1. Samarskii A. A. Theory of difference schemes. Moscow, 1989. 616 р. (in Russian).

2. Samarskii A. A., Gulin A. A. Numerical methods. Moscow, 1989. 432 р. (in Russian).

3. Matus P. P., Vo Thi Kim Tuyen, Gaspar F. Monotone difference schemes for linear parabolic equations with mixed boundary conditions. Doklady Natsional’noi akademii nauk Belarusi = Doklady of the National Academy of Sciences of Belarus, 2014, vol. 58, no. 5, pp. 18–22 (in Russian).

4. Arbogast T., Wheeler M. F., Yotov I. Mixed finite elements for elliptic problems with tensor coefficients as cell-centered finite differences. SIAM Journal on Numerical Analysis, 1997, vol. 34, no. 2, pp. 828–852. https://doi.org/10.1137/s0036142994262585

5. Crumpton P., Shaw G., Ware A. Discretization and multigrid solution of elliptic equations with mixed derivative terms and strongly discontinuous coefficients. Journal of Computational Physics, 1995, vol. 116, no. 2, pp. 343–358. https://doi.org/10.1006/jcph.1995.1032

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