Numerical integration in the discontinuous Galerkin method for elliptic problems
On the method of least squares of finding eigenvalues of some symmetric operators
Stability of the method of least squares for finding the eigenvalues of a symmetric operator
Error-estimates for the Ritz's method of finding eigenvalues and eigenfunctions
Error bounds for eigenvalues and eigenfunctions of some ordinary differential operators by the method of least squares
On the method of least squares of finding eigenvalues and eigenfunctions of some symmetric operators. II.
Error-estimates for the method of least squares of finding eigenvalues and eigenfunctions
Výuka matematické informatiky na matematicko-fyzikální fakultě UK
Wavelets
On the exact values of coefficients of coiflets
In 1989, R. Coifman suggested the design of orthonormal wavelet systems with vanishing moments for both scaling and wavelet functions. They were first constructed by I. Daubechies [15, 16], and she named them coiflets. In this paper, we propose a system of necessary conditions which is redundant free and simpler than the known system due to the elimination of some quadratic conditions, thus the construction of coiflets is simplified and enables us to find the exact values of the scaling coefficients...
On the finite element analysis of problems with nonlinear Newton boundary conditions in nonpolygonal domains
The paper is concerned with the study of an elliptic boundary value problem with a nonlinear Newton boundary condition considered in a two-dimensional nonpolygonal domain with a curved boundary. The existence and uniqueness of the solution of the continuous problem is a consequence of the monotone operator theory. The main attention is paid to the effect of the basic finite element variational crimes: approximation of the curved boundary by a polygonal one and the evaluation of integrals by numerical...
Prof. Dr. Jan Potoček osmdesátiletý
On a parabolic problem with nonlinear Newton boundary conditions
The paper is concerned with the study of a parabolic initial-boundary value problem with nonlinear Newton boundary condition considered in a two-dimensional domain. The goal is to prove the existence and uniqueness of a weak solution to the problem in the case when the nonlinearity in the Newton boundary condition does not satisfy any monotonicity condition and to analyze the finite element approximation.
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