Repin Sergey Igorevich

Publications in Math-Net.Ru

1. Solving differential equations by neural networks: goal functionals and verification of results
   
   Mat. Model., 36:6 (2024),  179–200
2. Estimates of errors generated by uncertain data in a coupled pieso-electric problem
   
   Zap. Nauchn. Sem. POMI, 539 (2024),  157–179
3. Derivation of fully computable error bounds from a posteriori error identities
   
   Zap. Nauchn. Sem. POMI, 539 (2024),  120–156
4. A posteriori error identities for the evolutionary Stokes problem
   
   Zap. Nauchn. Sem. POMI, 536 (2024),  261–285
5. A posteriori error estimates of approximate solutions to elliptic boundary value problems in terms of local norms and cost functionals
   
   Zh. Vychisl. Mat. Mat. Fiz., 64:12 (2024),  2270–2285
6. Identities for measures of deviation from solutions to parabolic-hyperbolic equations
   
   Zh. Vychisl. Mat. Mat. Fiz., 64:5 (2024),  819–834
7. A posteriori identities for measures of deviation from exact solutions of nonlinear boundary value problems
   
   Zh. Vychisl. Mat. Mat. Fiz., 63:6 (2023),  896–919
8. A posteriori error identities for parabolic convection–diffusion problems
   
   Zap. Nauchn. Sem. POMI, 519 (2022),  205–228
9. Error control for approximate solutions of a class of singularly perturbed boundary value problems
   
   Zh. Vychisl. Mat. Mat. Fiz., 62:11 (2022),  1822–1839
10. Error identities for parabolic initial boundary value problems
    
    Zap. Nauchn. Sem. POMI, 508 (2021),  147–172
11. A posteriori error control of approximate solutions to boundary value problems constructed by neural networks
    
    Zap. Nauchn. Sem. POMI, 499 (2021),  77–104
12. Identity for deviations from the exact solution of the problem $\Lambda^*\mathcal{A}\Lambda u+l=0$ and its implications
    
    Zh. Vychisl. Mat. Mat. Fiz., 61:12 (2021),  1986–2009
13. Estimates of the distance to the solution of an evolutionary problem obtained by linearization of the Navier–Stokes equation
    
    Zap. Nauchn. Sem. POMI, 489 (2020),  67–80
14. Biharmonic obstacle problem: guaranteed and computable error bounds for approximate solutions
    
    Zh. Vychisl. Mat. Mat. Fiz., 60:11 (2020),  1881–1897
15. Estimates of the deviation from exact solutions of boundary value problems in measures stronger than the energy norm
    
    Zh. Vychisl. Mat. Mat. Fiz., 60:5 (2020),  767–783
16. A posteriori estimates for the stationary Stokes problem in exterior domains
    
    Algebra i Analiz, 31:3 (2019),  184–215
17. On projectors to subspaces of vector valued functions subject to conditions of the divergence free type
    
    Zap. Nauchn. Sem. POMI, 459 (2017),  83–103
18. On variational representations of the constant in the inf sup condition for the Stokes problem
    
    Zap. Nauchn. Sem. POMI, 444 (2016),  110–123
19. Estimates of the distance to the set of divergence free fields
    
    Zap. Nauchn. Sem. POMI, 425 (2014),  99–116
20. Estimates of the distance to the exact solution of parabolic problems based on local Poincaré type inequalities
    
    Zap. Nauchn. Sem. POMI, 425 (2014),  7–34
21. Estimates of deviations from exact solution of the generalized Oseen problem
    
    Zap. Nauchn. Sem. POMI, 410 (2013),  110–130
22. Estimates of deviations from exact solution of the Stokes problem in the vorticity-velocity-pressure formulation
    
    Zap. Nauchn. Sem. POMI, 397 (2011),  73–88
23. Some Poincaré-type inequalities for functions of bounded deformation involving the deviatoric part of the symmetric gradient
    
    Zap. Nauchn. Sem. POMI, 385 (2010),  224–233
24. Estimates of deviations from exact solutions of variational problems with linear growth functionals
    
    Zap. Nauchn. Sem. POMI, 370 (2009),  132–150
25. Two-sided a posteriori error bounds for electro-magneto static problems
    
    Zap. Nauchn. Sem. POMI, 370 (2009),  94–110
26. A posteriori estimates for a generalized Stokes problem
    
    Zap. Nauchn. Sem. POMI, 362 (2008),  272–302
27. Functional a posteriori estimates for elliptic variational inequalities
    
    Zap. Nauchn. Sem. POMI, 348 (2007),  147–164
28. Functional a posteriori error estimates for the reaction-convection-diffusion problem
    
    Zap. Nauchn. Sem. POMI, 348 (2007),  127–146
29. Estimates of the deviation from the minimizer for variational problems with power growth functionals
    
    Zap. Nauchn. Sem. POMI, 336 (2006),  5–24
30. A Posteriori Error Estimates for Approximate Solutions of Linear Parabolic Problems
    
    Differ. Uravn., 41:7 (2005),  925–937
31. On error estimates for approximate solutions in problems of the linear theory of thermoelasticity
    
    Izv. Vyssh. Uchebn. Zaved. Mat., 2005, no. 1,  64–72
32. Estimates of deviation from the exact solutions for some boundary-value problems with incompressibilily condition
    
    Algebra i Analiz, 16:5 (2004),  124–161
33. Local a posteriori estimates for the Stokes problem
    
    Zap. Nauchn. Sem. POMI, 318 (2004),  233–245
34. On the estimate of deviations from the exact solution of the Reissner–Mindlin plate problem
    
    Zap. Nauchn. Sem. POMI, 310 (2004),  145–157
35. Estimates of deviations for generalized Newtonian fluids
    
    Zap. Nauchn. Sem. POMI, 288 (2002),  178–203
36. A posteriori error estimates for approximate solutions to boundary problem of elliptic equations
    
    Zh. Vychisl. Mat. Mat. Fiz., 42:12 (2002),  1774–1787
37. Estimates of deviations from exact solutions of elliptic variational inequalities
    
    Zap. Nauchn. Sem. POMI, 271 (2000),  188–203
38. A posteriori estimates for the accuracy of variational methods for problems with nonconvex functionals
    
    Algebra i Analiz, 11:4 (1999),  151–182
39. A posteriori estimates for the Stokes problem
    
    Zap. Nauchn. Sem. POMI, 259 (1999),  195–211
40. A posteriori error estimates for approximate solutions of variational problems with power growtn functionals
    
    Zap. Nauchn. Sem. POMI, 249 (1997),  244–255
41. A posteriori error estimation for nonlinear variational problems by duality theory
    
    Zap. Nauchn. Sem. POMI, 243 (1997),  201–214
42. Numerical modelling of discontinuous solution of perfectly elasto-plastic problems
    
    Mat. Model., 8:4 (1996),  113–127
43. A priori error estimates of variational-difference methods for Hencky plasticity problems
    
    Zap. Nauchn. Sem. POMI, 221 (1995),  226–234
44. On the approximation of solutions of variational problems in the theory of ideal plasticity
    
    Izv. Vyssh. Uchebn. Zaved. Mat., 1994, no. 9,  60–69
45. Variational formulations for discontinuous displacement fields in problems of ideal plasticity
    
    Dokl. Akad. Nauk SSSR, 320:6 (1991),  1340–1344
46. A variational-difference method of solving problems with functionals of linear growth
    
    Zh. Vychisl. Mat. Mat. Fiz., 29:5 (1989),  693–708
47. A variational difference method for solving problems of ideal plasticity in which discontinuities may appear
    
    Zh. Vychisl. Mat. Mat. Fiz., 28:3 (1988),  449–453
48. Minimization of a class of non-differentiable functionals by a relaxation method
    
    Zh. Vychisl. Mat. Mat. Fiz., 27:7 (1987),  976–983


49. Preface
    
    Zap. Nauchn. Sem. POMI, 536 (2024),  5–6
50. On the 90th birthday of Vsevolod Alekseevich Solonnikov
    
    Uspekhi Mat. Nauk, 78:5(473) (2023),  187–198
51. Preface
    
    Zap. Nauchn. Sem. POMI, 499 (2021),  5–6
52. To Solonnikov's jubilee
    
    Zap. Nauchn. Sem. POMI, 362 (2008),  5–14
53. To the jubillee of O. A. Ladyzhenskaya
    
    Zap. Nauchn. Sem. POMI, 288 (2002),  5–13