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

This article is cited in 8 scientific papers (total in 8 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.

DOI: https://doi.org/10.7868/S0044466914030041

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

Bibliographic databases:

UDC: 519.632
Received: 11.06.2013

Citation: R. Z. Dautov, E. M. Fedotov, “Abstract theory of hybridizable discontinuous Galerkin methods for second-order quasilinear elliptic problems”, Zh. Vychisl. Mat. Mat. Fiz., 54:3 (2014), 463–480; Comput. Math. Math. Phys., 54:3 (2014), 474–490

Citation in format AMSBIB
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    3. A. K. Volkov, N. A. Kudryashov, “Nonlinear waves described by a fifth-order equation derived from the Fermi–Pasta–Ulam system”, Comput. Math. Math. Phys., 56:4 (2016), 680–687  mathnet  crossref  crossref  mathscinet  isi  elib
    4. M. V. Vasileva, V. I. Vasilev, T. S. Timofeeva, “Chislennoe reshenie metodom konechnykh elementov zadach diffuzionnogo i konvektivnogo perenosa v silno geterogennykh poristykh sredakh”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 158, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2016, 243–261  mathnet  elib
    5. R. V. Zhalnin, V. F. Masyagin, Y. Y. Peskova, “A priori estimates of solution of a homogeneous boundary value problem for parabolic type equations by the discontinuous Galerkin method on staggered grids”, Mordovia Univ. Bull., 27:4 (2017), 490–503  crossref  mathscinet  isi
    6. M. Moon, H. K. Jun, T. Suh, “Error estimates on hybridizable discontinuous Galerkin methods for parabolic equations with nonlinear coefficients”, Adv. Math. Phys., 2017, 9736818  crossref  mathscinet  isi
    7. R. V. Zhalnin, V. F. Masyagin, “Apriornye otsenki dlya metoda Galerkina s razryvnymi bazisnymi funktsiyami na raznesennykh setkakh dlya odnorodnoi zadachi Dirikhle”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 11:2 (2018), 29–43  mathnet  crossref  elib
    8. R. V. Zhalnin, V. F. Masyagin, E. E. Peskova, V. F. Tishkin, “Apriornye otsenki lokalnogo razryvnogo metoda Galerkina na raznesennykh setkakh dlya resheniya uravneniya parabolicheskogo tipa v ramkakh odnorodnoi zadachi Dirikhle”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 24:1 (2020), 116–136  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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