(i) Theoretical and numerical analysis of the thermo-, piezo- and pyro-elasticity and their applications
(ii) Finite element method, a posteriori error estimators, lower and upper bounds of error estimations, h- and hp-adaptive finite element schemes
(iii) Programming of the finite element algorithms and numerical simulations

• Methods of computer calculations (cs)
• Software systems validation and verification (122 - cs)
• Industrial pre-diploma internship (122 – cs, masters)
• Scientific Seminar (122 - cs, master)

• Drebotiy R., Shynkarenko H. Modified heuristic criterion for parameterchoice for one stabilization scheme of the finite element method // Journal of Applied and Numerical Analysis 2024, Vol. 2, pp. 41-55. doi: 10.30970/ana.2024.2.41
• Drebotiy R.H., Shynkarenko H.A. Quantum-assisted hλ-adaptive finite element method // arXiv preprint arXiv:2411.12687, 2024. 13 pp. https://doi.org/10.48550/arXiv.2411.12687
• Drebotiy R. Heuristic choice of the regularization parameter for optimal stabilization of the finite element approximations / R. Drebotiy, H. Shynkarenko // Mathematical Methods and Physicomechanical Fields. – Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine. – Lviv, 2023,  Vol. 66, No. 1-2, 206–221. – https://doi.org/10.15407/mmpmf2023.66.1-2.206-221
• Drebotiy R. Fully parallel algorithm for solution of advection-reaction Cauchy problem in one finite element regularization scheme / R. Drebotiy, V. Stelmashchuk, H. Shynkarenko // Manufacturing Processes. Actual Problems.– Politechnika Opolska.– Opole, 2023.– Vol. 1.– Pp. 35-44.
• Kvasnytsya H. А., Shynkarenko H. А. Analysis of a problem of harmonic wave in elastic bodies and h-adaptive finite element // Journal of Mathematical Sciences, 2023, Vol. 270, No. 1, February, – pp. 59-75.
• Drebotiy R. Finite element analysis of Green-Lindsay thermopiezoelectricity time-dependent problem / R. Drebotiy, V. Stelmashchuk, H. Shynkarenko // Visnyk of the Lviv University. Series Appl.Math. and Informatics. – Lviv, 2023.–Issue 31. pp. 28-44
• Квасниця Г., Малашняк П., Шинкаренко Г. Порівняння h-адаптивних схем МСЕ різних порядків для одновимірних крайових задач // Вісник Львів. ун-ту. Сер. приклад. матем. інформ. 2022. Вип. 30. С. 45-59.
• Gurey V., Shynkarenko H., Kuzio H. Mathematical Model of the Thermoelasticity of the Surface Layer of Parts During Discontinuous Friction Treatment. In book: Advances in Design, Simulation and Manufacturing DSMIE 2021. P. 12-22.
• Квасниця Г.А., Шинкаренко Г.А. Аналіз задачі про гармонічні хвилі в пружних тілах і її h-адаптивна скінченноелементна апроксимація // Математичні методи та фізико-механічні поля, 2020, т. 63, № 1. С.52-64.
• Dyyak I., Horlatch V., Shynkarenko H. Formulation and Numerical Analysis of Acoustics Problems in Coupled Thermohydroelastic Systems // Proceedings of International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory, DIPED-2019. Lviv, Ukraine, 12-14 Sept. 2019. Lviv: IEEE, 2019. pp. 168-171.
• Stelmashchuk V.V., Shynkarenko H.A. Well-Posedness of the Lord-Shulman Variational Problem of Thermopiezoelectricity // Journal of Mathematical Sciences.– 2019. – Vol. 238. – No 2. – pp. 139-153.
• Drebotiy R., Shynkarenko H. Elementwise decomposition of a posteriori error estimator based on reference solution for hp-adaptive finite element method // Visnyk of the Lviv University. Series Appl.Math. and Informatics.– Lviv, 2018.– Issue 26.- Pp. 56-69
• Chyr I.A., Shynkarenko H.A. Well-Posedness of the Green-Lindsay Variational Problem of Thermoelasticity // Journal of Mathematical Sciences.– 2017. – Vol. 226. – No 1. – pp. 11-27.
• Drebotiy R., Shynkarenko H. On the application of the one hp-adaptive finite element strategy for nonsymmetric convection-diffusion-reaction problems // Journal of Numerical and Applied Mathematics.– 2017.– Issue 3(126). Pp. 48-60.
• Stelmashchuk V.V., Shynkarenko H.A. Finite element analysis of the Green-Lindsay thermopiezoelectricity time-harmonic problem // Visnyk of the Lviv University. Appl. Math. Comput. Science Series, 25 (2017). P. 136–147.
• Kvasnytsia H., Shynkarenko , Vasylyshyn B. Numerical analysis of the effectivity and robustness of a posteriori error estimators of finite element method for the torsional problem // Manufacturing Processes: Actual Problems-2017. Vol. 1. Basic science applications. –Opole: Politechnika Opolska, 2017. – P. 31–46.
• Ostapov O.Yu., Vovk O.V., Shynkarenko H.A. Computable two-sided a posteriori error estimates for h-adaptive finite element method // Advances in Mechanics: Theoretical, Computational and Interdisciplinary Issues.– London: Taylor & Francis Group, CRC Press, 2016. – P. 449-452.
• Vahin P.P., Malets’ R.B., Shynkarenko H.A. Variational formulation of the problem of nonstationary thermoelasticity for thin shells compliant to shears and compression // J. Math. Sci. – 2016. – 217, No. 3. – P. – 345–364.
• Shynkarenko H.A., Vovk O.V. Numerical modeling of spiral waves on surface carbon monoxide oxidation reaction // Manufacturing Process. Actual Problems-2015. – Opole : Politechnika Opolska. – – Vol. 1. – P. 91–112.
• Drebotiy R., Shynkarenko H. Symmetrization of diffusion-advection-reaction problem and hp-adaptive finite element approximations // Visnyk of the Lviv University. Appl. Math. Comput. Science Series, 23 (2015). P. 55–72.
• Ostapov O.Yu., Shynkarenko H.A., Vovk O.V. A posteriori error estimator and h-adaptive finite element method for diffusion-advection-reaction problems // Recent Advances in Computational Mechanics. – London: Taylor & Francis Group, 2014. – P. 329–337.
• Drebotiy R., Shynkarenko H. Comparison of error indicators and refinement criteria for hp-adaptation algorithm for finite element method // Visnyk Odeskoho Natsionalnoho Universytetu. Matematyka i Mekhanika.– Odessa, 2014.– V.19, Is. 4(24).– Pp. 45–57.
• Trushevsky V., Shynkarenko G., Shcherbyna N. Finite Element Method and Artificial Neural Networks. Theoretical aspects and applications: Monograph // Lviv I. Franko University, 2014. – 396 p.
• Malets R., Shynkarenko H. Modeling and solvitability of the variational problem of thermo-elastic thin shells, compliant to shear and compression // Manufacturing Processes. Actual Problems – 2014. Vol.1. Basic Science Applications. Opole: Politechnika Opolska, 2014. pp.
• Vovk O.V., Shynkarenko A. Integration of Newton linearization into the time discretization of initial-boundary-value problems // J. Math. Sciences. – 2014. – V. 203, № 1. – С. 70–86.
• Horlatch V., Klymenko I., Shynkarenko H. Finite element analysis of forced steady-state thermoacoustic waves in dissipative fluid // Manufacturing Processes. Actual Problems – 2013. Vol.1. Basic Science Applications. Opole: Politechnika Opolska, 2013. pp. 47-66.
• Ostapov O.Yu., Shynkarenko H.A., Vovk O.V. Finite element adaptive refinement techniques for diffusion-advection-reaction problems // Manufacturing Processes: Actual Problems-2013. Vol. 1. Basic science applications. –Opole: Politechnika Opolska, 2013. – P. 31–46.
• Horlatch V., Klymenko I., Shynkarenko G. Formulation and well-posedness of the variational problem of viscous heat-conducting fluid acoustics // Journal of Numerical and Applied Mathematics – 2012. № 3 (109). – C. 53-71.
• Computer Technics. Computer Technologies // Textbook. 3-rd ed.- Kyiv:Karavella, 2011.-592 p. (in Ukrainian, with a group of authors)
• Ostapov O.Yu., Shynkarenko H.A. A posteriori error estimator for diffusion-advection-reaction boundary value problems: piecewise linear approximation on triangles // Numer. Appl. Math., 2 (2011). – P. 111–123.

In Lviv University:

since 2024, professor of the Department of Information Systems;
in 1995, he founded and until 2024 headed the Department of Information Systems;
1993-95 Professor, Department of Applied Mathematics;
1979-93 Associate professor, Department of Applied Mathematics;
1976-79 Assistant professor, Department of Applied Mathematics;
1973-76 Postgraduate student, Department of Applied Mathematics;
1971-73 Engineer-mathematician-programmer, Computer Center;
1966-71 Student of Mechanics and Mathematics Faculty.

1st semester
2nd semester