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

Zh. Vychisl. Mat. Mat. Fiz., 2014 Volume 54, Number 3, Pages 463–480 (Mi zvmmf10007)

This article is cited in 11 papers

Abstract theory of hybridizable discontinuous Galerkin methods for second-order quasilinear elliptic problems

R. Z. Dautov, E. M. Fedotov

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

Abstract: An abstract theory for discretizations of second-order quasilinear elliptic problems based on the mixed-hybrid discontinuous Galerkin method. Discrete schemes are formulated in terms of approximations of the solution to the problem, its gradient, flux, and the trace of the solution on the interelement boundaries. Stability and optimal error estimates are obtained under minimal assumptions on the approximating space. It is shown that the schemes admit an efficient numerical implementation.

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

UDC: 519.632

Received: 11.06.2013

DOI: 10.7868/S0044466914030041


 English version:
Computational Mathematics and Mathematical Physics, 2014, 54:3, 474–490

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