On Křížek’s decomposition of a polyhedron into convex components and its applications in the proof of a general Ostrogradskij’s theorem
The use of semiregular finite elements
Some new convergence results in finite element theories for elliptic problems
Hermite interpolation on simplexes in the finite element method
Finite element methods for linear coupled thermoelasticity
A general theorem on triangular finite -elements
Discrete forms of Friedrichs' inequalities in the finite element method
Finite element methods for coupled thermoelasticity and coupled consolidation of clay
How to avoid the use of Green's theorem in the Ciarlet-Raviart theory of variational crimes
Finite Element Variational Crimes in Parabolic-Elliptic Problems. Part I. Nonlinear Schemes.
The finite element method for nonlinear elliptic equations with discontinuous coefficients.
Třicet let matematické teorie metody konečných prvků (medailon prof. M. Zlámala)
Tetrahedral finite -elements
Finite element variational crimes in the case of semiregular elements
The finite element method for a strongly elliptic mixed boundary value problem is analyzed in the domain whose boundary is formed by two circles , with the same center and radii , , where . On one circle the homogeneous Dirichlet boundary condition and on the other one the nonhomogeneous Neumann boundary condition are prescribed. Both possibilities for are considered. The standard finite elements satisfying the minimum angle condition are in this case inconvenient; thus triangles obeying...
Green's theorem from the viewpoint of applications
Making use of a line integral defined without use of the partition of unity, Green’s theorem is proved in the case of two-dimensional domains with a Lipschitz-continuous boundary for functions belonging to the Sobolev spaces .
The late Professor Karel Rektorys
Extensions from the Sobolev spaces satisfying prescribed Dirichlet boundary conditions
Extensions from into (where ) are constructed in such a way that extended functions satisfy prescribed boundary conditions on the boundary of . The corresponding extension operator is linear and bounded.
On a generalization of Nikolskij's extension theorem in the case of two variables
A modification of the Nikolskij extension theorem for functions from Sobolev spaces is presented. This modification requires the boundary to be only Lipschitz continuous for an arbitrary ; however, it is restricted to the case of two-dimensional bounded domains.
Surface integral and Gauss-Ostrogradskij theorem from the viewpoint of applications
Making use of a surface integral defined without use of the partition of unity, trace theorems and the Gauss-Ostrogradskij theorem are proved in the case of three-dimensional domains with a Lipschitz-continuous boundary for functions belonging to the Sobolev spaces . The paper is a generalization of the previous author’s paper which is devoted to the line integral.
Nonhomogeneous boundary conditions and curved triangular finite elements
Approximation of nonhomogeneous boundary conditions of Dirichlet and Neumann types is suggested in solving boundary value problems of elliptic equations by the finite element method. Curved triangular elements are considered. In the first part of the paper the convergence of the finite element method is analyzed in the case of nonhomogeneous Dirichlet problem for elliptic equations of order , in the second part of the paper in the case of nonhomogeneous mixed boundary value problem for second order...
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