Analytic Extended Monosplines.
Analytic Representations Suitable for Numerical Computation of Some Special Functions.
Analytical and numerical methods for the CMKdV-II equation.
Analytical approximation to solutions of singularly perturbed boundary value problems.
Analytical solution of rotationally symmetric Stokes flow near corners
We present analytical solution of the Stokes problem in rotationally symmetric domains. This is then used to find the asymptotic behaviour of the solution in the vicinity of corners, also for Navier-Stokes equations. We apply this to construct very precise numerical finite element solution.
Analytical techniques for a numerical solution of the linear Volterra integral equation of the second kind.
Angiogenesis process with vessel impairment for Gompertzian and logistic type of tumour growth
We propose two models of vessel impairment in the process of tumour angiogenesis and we consider three types of treatment: standard chemotherapy, antiangiogenic treatment and a combined treatment. The models are based on the idea of Hahnfeldt et al. that the carrying capacity for any solid tumour depends on its vessel density. In the models proposed the carrying capacity also depends on the process of vessel impairment. In the first model a logistic type equation is used to describe the neoplastic...
Anisotropic -adaptive method based on interpolation error estimates in the -seminorm
We develop a new technique which, for the given smooth function, generates the anisotropic triangular grid and the corresponding polynomial approximation degrees based on the minimization of the interpolation error in the broken -seminorm. This technique can be employed for the numerical solution of boundary value problems with the aid of finite element methods. We present the theoretical background of this approach and show several numerical examples demonstrating the efficiency of the proposed...
Anisotropic interpolation error estimates via orthogonal expansions
We prove anisotropic interpolation error estimates for quadrilateral and hexahedral elements with all possible shape function spaces, which cover the intermediate families, tensor product families and serendipity families. Moreover, we show that the anisotropic interpolation error estimates hold for derivatives of any order. This goal is accomplished by investigating an interpolation defined via orthogonal expansions.
Anisotropic mesh adaption: application to computational fluid dynamics
In this communication we focus on goal-oriented anisotropic adaption techniques. Starting point has been the derivation of suitable anisotropic interpolation error estimates for piecewise linear finite elements, on triangular grids in . Then we have merged these interpolation estimates with the dual-based a posteriori error analysis proposed by R. Rannacher and R. Becker. As examples of this general anisotropic a posteriori analysis, elliptic, advection-diffusion-reaction and the Stokes problems...
Anisotropic mesh refinement in polyhedral domains: error estimates with data in L2(Ω)
The paper is concerned with the finite element solution of the Poisson equation with homogeneous Dirichlet boundary condition in a three-dimensional domain. Anisotropic, graded meshes from a former paper are reused for dealing with the singular behaviour of the solution in the vicinity of the non-smooth parts of the boundary. The discretization error is analyzed for the piecewise linear approximation in the H1(Ω)- and L2(Ω)-norms by using a new quasi-interpolation operator. This new interpolant...
Anmerkungen zu einem Mehrgitterverfahren für lineare Komplementaritätsprobleme.
Another formulation of the Wick’s theorem. Farewell, pairing?
The algebraic formulation of Wick’s theorem that allows one to present the vacuum or thermal averages of the chronological product of an arbitrary number of field operators as a determinant (permanent) of the matrix is proposed. Each element of the matrix is the average of the chronological product of only two operators. This formulation is extremely convenient for practical calculations in quantum field theory, statistical physics, and quantum chemistry by the standard packages of the well known...
Ansätze für einen intervallmathematischen bzw. logisch dreiwertigen Aufbau der analytischen Geometrie
Anwendungen des Fixpunktsatzes für Pseudometrische Räume in der Intervallrechnung.
Apollo 13 Risk Assessment Revisited
Fault tree methodology is the most widespread risk assessment tool by which one is able to predict - in principle - the outcome of an event whenever it is reduced to simpler ones by the logic operations conjunction and disjunction according to the basics of Boolean algebra. The object of this work is to present an algorithm by which, using the corresponding computer code, one is able to predict - in practice - the outcome of an event whenever its fault tree is given in the usual form.
Aposteriorní odhady chyby v metodě konečných prvků
Application de la théorie des fonctions convexes d'ordre supérieur à l'étude de certains procédés d'intégration numérique des équations différentielles
Application de l'approximation stochastique à la détermination des masques pour la lecture automatique de caractères imprimés
Application de l'optimisation en nombres entiers à un problème d'«arrondissage»