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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2013 Volume 53, Number 11, Pages 1791–1803 (Mi zvmmf9942)

This article is cited in 3 papers

Discontinuous mixed penalty-free Galerkin method for second-order quasilinear elliptic equations

R. Z. Dautov, E. M. Fedotov

Kazan Federal University, ul. Kremlevskaya 18, Kazan, 420008, Tatarstan, Russia

Abstract: Discrete schemes for finding an approximate solution of the Dirichlet problem for a second-order quasilinear elliptic equation in conservative form are investigated. The schemes are based on the discontinuous Galerkin method (DG schemes) in a mixed formulation and do not involve internal penalty parameters. Error estimates typical of DG schemes with internal penalty are obtained. A new result in the analysis of the schemes is that they are proved to satisfy the Ladyzhenskaya–Babuska–Brezzi condition (inf-sup) condition.

Key words: discontinuous Galerkin method, mixed method, quasilinear elliptic equations, error estimate, LBB condition.

UDC: 519.632.4

Received: 21.02.2013
Revised: 22.05.2013

DOI: 10.7868/S0044466913110021


 English version:
Computational Mathematics and Mathematical Physics, 2013, 53:11, 1614–1625

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© Steklov Math. Inst. of RAS, 2025