numerical methods for solving partial differential equations, finite element method,
mechanics of solid bodies.
Main publications:
V.G. Korneev, Skhemy metoda konechnykh elementov vysokikh poryadkov tochnosti, Izd-vo Leningradskogo gos. universiteta, L., 1977
V. Korneev and U. Langer, Approximate solution of theory of plastic flow theory problems., Teubner-Texte fur Mathematik, 69, BSB B.G. Teubner Verlagsgesellschaft, Leipzig, 1984
V. Korneev and U. Langer, “Domain Decomposition Methods and Precon-ditioning”, Encyclopedia of Computational Mechanics, 1 (2004), 617–647, John Wiley & Sons, Ltd
V.G. Korneev, I.E. Anufriev, V.S. Kostylev, “Exactly equilibrated fields, can they be efficiently used for a posteriori error estimation?”, Uchenye zapiski Kazanskogo gos. universiteta. Seriya fiziko-matematicheskie nauki, 148:4 (2006), 94–143
V. Korneev, A. Rytov, “Diskretizatsii trekhmernykh ellipticheskikh kraevykh zadach spektralnymi elementami i metody dekompozitsii oblasti”, Zhurnal vychislitelnoi matematiki i matem. fiziki, 47:10 (2007), 1754–1772
V. G. Korneev, “A posteriori error majorants for numerical solutions of plate bending problems on a Winkler basis”, Sib. Zh. Vychisl. Mat., 26:1 (2023), 43–55
2020
2.
V. G. Korneev, “A note on a posteriori error bounds for numerical solutions of elliptic equations with a piecewise constant reaction coefficient having large jumps”, Zh. Vychisl. Mat. Mat. Fiz., 60:11 (2020), 1815–1822; Comput. Math. Math. Phys., 60:11 (2020), 1754–1760
V. G. Korneev, “On error control in the numerical solution of reaction–diffusion equation”, Zh. Vychisl. Mat. Mat. Fiz., 59:1 (2019), 3–20; Comput. Math. Math. Phys., 59:1 (2019), 1–18
V. G. Korneev, “On domain decomposition preconditioner of BPS type for finite element discretizations of 3D elliptic equations”, Zh. Vychisl. Mat. Mat. Fiz., 52:9 (2012), 1655; Comput. Math. Math. Phys., 52:9 (2012), 1260–1294
V. G. Korneev, “Simple algorithms for calculation of the classical a posteriori error estimates of numerical solutions of elliptic equations”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 153:4 (2011), 11–27
I. E. Anufriev, V. G. Korneev, V. S. Kostylev, “Exactly equilibrated fields, can they be efficiently used for a posteriori error estimation?”, Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki, 148:4 (2006), 94–143
I. E. Anufriev, V. G. Korneev, “Numerical testing of a decomposition method for the $p$-version of the finite element method”, Izv. Vyssh. Uchebn. Zaved. Mat., 2005, no. 1, 10–24; Russian Math. (Iz. VUZ), 49:1 (2005), 7–20
V. G. Korneev, “Local Dirichlet problems on subdomains of decomposition in $HP$-discretizations, and optimal algorithms for their solution”, Matem. Mod., 14:5 (2002), 51–74
V. G. Korneev, “An Almost Optimal Method for Dirichlet Problems on Decomposition Subdomains of the Hierarchical hp-Version”, Differ. Uravn., 37:7 (2001), 959–968; Differ. Equ., 37:7 (2001), 1008–1018
V. G. Korneev, Ya. Fish, “Two-level methods, based on aggregation, for solving three-dimensional problems”, Izv. Vyssh. Uchebn. Zaved. Mat., 2000, no. 11, 42–61; Russian Math. (Iz. VUZ), 44:11 (2000), 39–57
V. G. Korneev, S. Ensen, “Efficient pre-conditioning by the domain decomposition method for the $p$-version with a hierarchical basis. II”, Izv. Vyssh. Uchebn. Zaved. Mat., 1999, no. 11, 24–40; Russian Math. (Iz. VUZ), 43:11 (1999), 22–37
V. G. Korneev, S. Ensen, “Efficient preconditioning by the domain decomposition method for the $p$-version with a hierarchical basis. I”, Izv. Vyssh. Uchebn. Zaved. Mat., 1999, no. 5, 37–56; Russian Math. (Iz. VUZ), 43:5 (1999), 35–52
V. G. Korneev, S. A. Ivanov, “Preconditioning in the domain decomposition methods for the $p$-version with the hierarchical bases”, Matem. Mod., 8:9 (1996), 63–73
D. Bahlmann, V. G. Korneev, “A fast solver for the clamped plate problem in a rectangle based on a boundary potentials method”, Zh. Vychisl. Mat. Mat. Fiz., 36:7 (1996), 174–190; Comput. Math. Math. Phys., 36:7 (1996), 969–982
1995
18.
S. A. Ivanov, V. G. Korneev, “Choice of high order coordinate functions and preconditioning in frames of the method of domain decomposition”, Izv. Vyssh. Uchebn. Zaved. Mat., 1995, no. 4, 62–81; Russian Math. (Iz. VUZ), 39:4 (1995), 58–76
B. Weber, V. G. Korneev, “A preconditioner of a finite-element matrix for a fourth-order elliptic equation”, Zh. Vychisl. Mat. Mat. Fiz., 33:3 (1993), 364–379; Comput. Math. Math. Phys., 33:3 (1993), 329–341
1991
20.
S. A. Ivanov, V. G. Korneev, “The problem of the thermal emission of a shell taking internal reflection into account”, Zh. Vychisl. Mat. Mat. Fiz., 31:1 (1991), 132–142; U.S.S.R. Comput. Math. Math. Phys., 31:1 (1991), 92–100
1989
21.
V. G. Korneev, “Schemes for solving elliptic differential equations of order $2n$, $n\ge 2$, with incompatible curvilinear finite elements near the boundary”, Zh. Vychisl. Mat. Mat. Fiz., 29:4 (1989), 483–496; U.S.S.R. Comput. Math. Math. Phys., 29:2 (1989), 102–111
1988
22.
S. A. Ivanov, V. G. Korneev, Ĭ. Lang, “Estimates of constants in inequalities for basis elements”, Zh. Vychisl. Mat. Mat. Fiz., 28:9 (1988), 1425–1431; U.S.S.R. Comput. Math. Math. Phys., 28:5 (1988), 97–101
1986
23.
V. G. Korneev, K. A. Khusanov, “Curvilinear finite elements of the class $C_1$ with singular coordinate functions”, Differ. Uravn., 22:12 (1986), 2144–2157
V. G. Korneev, U. Langer, “Regularity of solutions of problems of the theory of plastic flow”, Differ. Uravn., 20:4 (1984), 667–676
1982
25.
V. G. Korneev, “Superconvergence of solutions of the finite-element method in mesh norms”, Zh. Vychisl. Mat. Mat. Fiz., 22:5 (1982), 1133–1148; U.S.S.R. Comput. Math. Math. Phys., 22:5 (1982), 115–131
V. G. Korneev, “Numerical solution in terms of stress of problems in the theory of shells using an oblique-angled grid”, Zh. Vychisl. Mat. Mat. Fiz., 21:2 (1981), 441–451; U.S.S.R. Comput. Math. Math. Phys., 21:2 (1981), 184–194
V. G. Korneev, “Solution by the finite element method of problems of the theory of plastic flow for earth structures”, Differ. Uravn., 16:4 (1980), 705–722
29.
V. G. Korneev, “Approximate solution of the theory of plastic flow for media subject to Coulomb's yield criterion”, Zh. Vychisl. Mat. Mat. Fiz., 20:2 (1980), 433–450; U.S.S.R. Comput. Math. Math. Phys., 20:2 (1980), 165–181
V. G. Korneev, “High-order schemes of the finite elements method for second-order elliptic equations in three-dimensional domains. II”, Zh. Vychisl. Mat. Mat. Fiz., 19:5 (1979), 1141–1148; U.S.S.R. Comput. Math. Math. Phys., 19:5 (1979), 54–61
31.
V. G. Korneev, “Schemes of the finite element method of high orders of accuracy for second-order elliptic equations in three-dimensional regions — I”, Zh. Vychisl. Mat. Mat. Fiz., 19:4 (1979), 937–949; U.S.S.R. Comput. Math. Math. Phys., 19:4 (1979), 149–162
V. G. Korneev, “Iterative methods for the solution of the systems of equations of the finite element method”, Zh. Vychisl. Mat. Mat. Fiz., 17:5 (1977), 1213–1233; U.S.S.R. Comput. Math. Math. Phys., 17:5 (1977), 109–129
V. G. Korneev, S. E. Ponomarev, “Solution of the plastic flow theory problem by the finite element method”, Zh. Vychisl. Mat. Mat. Fiz., 17:2 (1977), 437–452; U.S.S.R. Comput. Math. Math. Phys., 17:2 (1977), 144–160
1974
35.
V. G. Korneev, “Theorem on the positive definiteness of a differential operator in the theory of thin nonsloping shells”, Dokl. Akad. Nauk SSSR, 218:6 (1974), 1291–1293
2003
36.
V. G. Korneev, “Letter to the Editorial Board”, Differ. Uravn., 39:2 (2003), 284; Differ. Equ., 39:2 (2003), 311
1996
37.
Yu. K. Demjanovich, V. G. Korneev, “Foreword”, Matem. Mod., 8:9 (1996), 2