Main scientific results

1979

Construction of a nonconvex octahedron with non-Lipschitzian boundary [J4].

1980

The unisolvency of the composite tetrahedral stress finite element from 

H^3x3_sym(Div) with 42 degrees of freedom [J4], [C1].

1981

The hydraulic resistance of oil transformer windings [H1].

1982

Existence of a strongly regular family of decompositions of an arbitrary polyhedron into tetrahedra [C1].

1983

Construction of divergence-free finite element basis functions with small supports [B1] (for continuous piecewise linear divergence-free basis functions see [B9]).

1984

Superconvergence phenomenon in the finite element method arising from averaging gradients [B3].

1985

Dual finite element method for the biharmonic problem [C5].

1986

Construction of divergence-free finite element functions in three-dimensional domains [B4].

1987

A general definition of superconvergence [B6].

1988 

O(h⁴)-superconvergence of piecewise bilinear finite element approximations [B7], [B8].

1989

Finite element solution of time-harmonic Maxwell equations [C11].

1990

Preconditioned biconjugate gradient method for a system of linear algebraic equations in a complex variable [G5], [B20].

1991

The maximum angle condition that guarantees optimal interpolation properties of linear triangular finite elements [C12].

1992

The maximum angle condition that guarantees optimal interpolation properties of linear tetrahedral finite elements [B11].

1993

Numerical analysis of finite element variational crimes for a nonlinear elliptic problem [B14].

1994

Finite element analysis of a quasilinear nonpotential elliptic problem of a nonmonotone type [B19].

1995

Discrete maximum principle on tetrahedral meshes [B21], [B34], [B35].

1996

A comparison principle for a quasilinear elliptic problem [B25].

1997

Local refinements of unstructured tetrahedral meshes [B26].

1998

Finite element analysis of a radiation heat transfer problem [B29].

1999

Finite speed of gravitational interaction contributes to the expansion of the universe [B32].

2000

Numerical analysis of variational crimes for a quasilinear elliptic problem in 3D [B33].

2001

The Springer monograph: 17 lectures on Fermat numbers [A5].

2002

Colouring polytopic partitions [C25], in particular, any tetrahedralization is   f o u r - c o l o u r a b l e .

2003

The nonexistence of a Lobachevsky geometry model of an isotropic and homogeneous universe [B41] (for the time-lens principle see [K25]).

2004

A new relationship between Mersenne and Sophie Germain primes [B46].

2005 

For a given integer m there is no face-to-face tetrahedralization of R³ such that each edge is surrounded by m tetrahedra [B50].

2006 

There is no face-to-face partition of R⁵ into acute simplices [B54].

2007 

Dissection of the path-simplex in Rⁿ into n path-simplices [B56].

2008

Euclidean primes have the minimum number of primitive roots [B60].

2009

Gravitational aberration contributes to the dark energy necessary for the accelerated expansion of the Universe [B61].

2010

Nodal superconvergence by averaging [B67].

2011

Two-sided bounds of the FE discretization error [B75].

2012

Maximum angle condition is not necessary for convergence of the finite element method [B79].

2013

Higher order numerical integration formulae on pyramids [B85].

2014

Dark matter is mainly a modelling error [B91].

2015

Manifestations of dark energy in the Solar system [B95], [A22].

2016

Excessive extrapolations in cosmology [B100].

2017

Maximum angle condition for n-simplices [C36].

2018

Ten arguments against the proclaimed amount of dark matter [B108].

2019

Ten significant problems and drawbacks of Einstein's equations [B111].

2020

The Springer monograph: Simplical partitions with applications to the finite element method [A27].

2021

The Springer monograph: From great discoveries in number theory to applications [A29].

2022

Why masses of binary black hole mergers are overestimated [B121].

2023

The Springer monograph: Mathematical aspects of paradoxes in cosmology. Can mathematics explain the contemporary cosmological crisis? [A31].

2024

There exist four regular tessellations of a three-dimensional maximally symmetric hyperbolic manifold by regular curved polyhedra [B129].