Bosko Jovanovic - Academia.edu (original) (raw)
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Papers by Bosko Jovanovic
Annals of the New York Academy of Sciences, 2005
Theoretical and Applied Mechanics, 2021
The paper describes the flow of a suspension which is a mixture of two phases: liquid and solid g... more The paper describes the flow of a suspension which is a mixture of two phases: liquid and solid granules. The continuum model with microstructure is introduced, which involves two independent kinematic quantities: the velocity vector and the micro-rotation vector. The physical analogy is based on the movement of the suspension between two coaxial cylinders. The inner cylinder is stationary and the outer one rotates with constant angular velocity. This physical analogy enabled a mathematical model in a form of two coupled differential equations with variable coefficients. The aim of the paper is to present the numerical aspect of the solution for this complex mathematical model. It is assumed that the solid granules are identically oriented and that under the influence of the fluid they move translationally or rotate around the symmetry axis but the direction of their symmetry axes does not change. The solution was obtained by the ordinary finite difference method, and then the corre...
In this paper, we consider a non-standard parabolic transmission problem in disjoint domains. A p... more In this paper, we consider a non-standard parabolic transmission problem in disjoint domains. A priori estimate for its weak solution in appropriate Sobolev-like space is proved. The convergence of a factorized finite difference scheme approximating this problem is analyzed.
Computational Methods in Applied Mathematics, 2004
A survey of the results concerning the convergence of finite difference schemes for boundary value... more A survey of the results concerning the convergence of finite difference schemes for boundary value problems with generalized solutions from the Sobolev space is presented. In particular, difference schemes for some problems with singular coefficients are investigated.
Filomat, 2017
An additive finite-difference scheme for numerical approximation of initial-boundary value proble... more An additive finite-difference scheme for numerical approximation of initial-boundary value problem for two-dimensional fractional in time diffusion equation is proposed. Its stability is investigated and a convergence rate estimate is obtained.
AIP Conference Proceedings, 2009
We consider a nonlinear elliptic boundary value problem, which describes a radiative heat transfe... more We consider a nonlinear elliptic boundary value problem, which describes a radiative heat transfer. This paper is concerned with the solution of the nonlinear system of equations arising from FEM approximations of the problem. We employ Newton’s method to develop a new version of the two‐grid method originated from O. Axelson and J. Xu. Numerical results are given to a simple problem with exact solution and to a simplified version of the physical problem.
Publications de l'Institut Mathematique, 2016
Lecture Notes in Computer Science, 1997
In this work we expose a methodology for establishing convergence rate estimates for finite diffe... more In this work we expose a methodology for establishing convergence rate estimates for finite difference schemes based on the interpolation theory of Banach spaces. As a model problem we consider Dirichlet boundary value problem for second order linear elliptic equation with variable coefficients from Sobolev spaces. Using interpolation theory we construct fractional-order convergence rate estimates which are consistent with the smoothness of data.
Lecture Notes in Computer Science, 2005
... where ξ = (ξ1,ξ2), MU = − 2 ∑ i,j=1 Aij(ξ) ∂2U ∂ξi∂ξj + 2 2 ∑ i=1 Bi(ξ) ∂U ∂ξi + C(ξ)U , Aij(... more ... where ξ = (ξ1,ξ2), MU = − 2 ∑ i,j=1 Aij(ξ) ∂2U ∂ξi∂ξj + 2 2 ∑ i=1 Bi(ξ) ∂U ∂ξi + C(ξ)U , Aij(ξ) = Aji(ξ) is elliptic operator and δS(ξ) is Dirac distribution concentrated on S. The equal-ity in (1) is treated in the sense of distributions. ... 2 ∑ i=1 [ bi ∂u ∂xi + ∂(biu) ∂xi ] + cu , (4) ...
Lecture Notes in Computer Science, 2009
Lecture Notes in Computer Science, 2009
Lecture Notes in Computer Science
We study numerical approximations of weak solutions of hyperbolic problems with discontinuous coe... more We study numerical approximations of weak solutions of hyperbolic problems with discontinuous coefficients and nonlinear source terms in the equation. By a semidiscretization of a Dirichlet problem in the space variable we obtain a system of ordinary differential equations (SODEs), which is expected to be an approximation of the original problem. We show at conditions similar to those for the hyperbolic problem, that the solution of the SODEs blows up. Under certain assumptions, we also prove that the numerical blow-up time converges to the real blow-up time when the mesh size goes to zero. Numerical experiments are analyzed.
PAMM, 2005
Paper deals with the construction of a priori estimates for the solution of Cauchy problem for an... more Paper deals with the construction of a priori estimates for the solution of Cauchy problem for an abstract linear differential equation in Hilbert space under perturbations of the initial condition, right‐hand side, and operators of the problem. It is shown that a priori estimates of strong stability can be obtained directly on the basis of various a priori estimates for the solution of the Cauchy problem. The perturbations of the operators of the problem are estimated in the corresponding operator norms. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Mathematics of Computation, 1985
Springer Optimization and Its Applications, 2010
In this paper we investigate an initial boundary value problem for a one-dimensional hyperbolic e... more In this paper we investigate an initial boundary value problem for a one-dimensional hyperbolic equation in two disjoint intervals. A finite difference scheme approximating this initial boundary value problem is proposed and analyzed. An estimate of the convergence rate is obtained.
Numerische Mathematik, 1989
SummaryWe study the convergence of the finite-difference schemes for the first initial-boundary v... more SummaryWe study the convergence of the finite-difference schemes for the first initial-boundary value problem for linear second-order parabolic equations with variable coefficients. Using the bilinear version of the Bramble-Hilbert lemma we obtain estimate of convergence, in discreteW21, 1/2 norm, compatible with the smoothness of generalized solutionu∈W2λ, λ/2 (Q) (1
Annals of the New York Academy of Sciences, 2005
Theoretical and Applied Mechanics, 2021
The paper describes the flow of a suspension which is a mixture of two phases: liquid and solid g... more The paper describes the flow of a suspension which is a mixture of two phases: liquid and solid granules. The continuum model with microstructure is introduced, which involves two independent kinematic quantities: the velocity vector and the micro-rotation vector. The physical analogy is based on the movement of the suspension between two coaxial cylinders. The inner cylinder is stationary and the outer one rotates with constant angular velocity. This physical analogy enabled a mathematical model in a form of two coupled differential equations with variable coefficients. The aim of the paper is to present the numerical aspect of the solution for this complex mathematical model. It is assumed that the solid granules are identically oriented and that under the influence of the fluid they move translationally or rotate around the symmetry axis but the direction of their symmetry axes does not change. The solution was obtained by the ordinary finite difference method, and then the corre...
In this paper, we consider a non-standard parabolic transmission problem in disjoint domains. A p... more In this paper, we consider a non-standard parabolic transmission problem in disjoint domains. A priori estimate for its weak solution in appropriate Sobolev-like space is proved. The convergence of a factorized finite difference scheme approximating this problem is analyzed.
Computational Methods in Applied Mathematics, 2004
A survey of the results concerning the convergence of finite difference schemes for boundary value... more A survey of the results concerning the convergence of finite difference schemes for boundary value problems with generalized solutions from the Sobolev space is presented. In particular, difference schemes for some problems with singular coefficients are investigated.
Filomat, 2017
An additive finite-difference scheme for numerical approximation of initial-boundary value proble... more An additive finite-difference scheme for numerical approximation of initial-boundary value problem for two-dimensional fractional in time diffusion equation is proposed. Its stability is investigated and a convergence rate estimate is obtained.
AIP Conference Proceedings, 2009
We consider a nonlinear elliptic boundary value problem, which describes a radiative heat transfe... more We consider a nonlinear elliptic boundary value problem, which describes a radiative heat transfer. This paper is concerned with the solution of the nonlinear system of equations arising from FEM approximations of the problem. We employ Newton’s method to develop a new version of the two‐grid method originated from O. Axelson and J. Xu. Numerical results are given to a simple problem with exact solution and to a simplified version of the physical problem.
Publications de l'Institut Mathematique, 2016
Lecture Notes in Computer Science, 1997
In this work we expose a methodology for establishing convergence rate estimates for finite diffe... more In this work we expose a methodology for establishing convergence rate estimates for finite difference schemes based on the interpolation theory of Banach spaces. As a model problem we consider Dirichlet boundary value problem for second order linear elliptic equation with variable coefficients from Sobolev spaces. Using interpolation theory we construct fractional-order convergence rate estimates which are consistent with the smoothness of data.
Lecture Notes in Computer Science, 2005
... where ξ = (ξ1,ξ2), MU = − 2 ∑ i,j=1 Aij(ξ) ∂2U ∂ξi∂ξj + 2 2 ∑ i=1 Bi(ξ) ∂U ∂ξi + C(ξ)U , Aij(... more ... where ξ = (ξ1,ξ2), MU = − 2 ∑ i,j=1 Aij(ξ) ∂2U ∂ξi∂ξj + 2 2 ∑ i=1 Bi(ξ) ∂U ∂ξi + C(ξ)U , Aij(ξ) = Aji(ξ) is elliptic operator and δS(ξ) is Dirac distribution concentrated on S. The equal-ity in (1) is treated in the sense of distributions. ... 2 ∑ i=1 [ bi ∂u ∂xi + ∂(biu) ∂xi ] + cu , (4) ...
Lecture Notes in Computer Science, 2009
Lecture Notes in Computer Science, 2009
Lecture Notes in Computer Science
We study numerical approximations of weak solutions of hyperbolic problems with discontinuous coe... more We study numerical approximations of weak solutions of hyperbolic problems with discontinuous coefficients and nonlinear source terms in the equation. By a semidiscretization of a Dirichlet problem in the space variable we obtain a system of ordinary differential equations (SODEs), which is expected to be an approximation of the original problem. We show at conditions similar to those for the hyperbolic problem, that the solution of the SODEs blows up. Under certain assumptions, we also prove that the numerical blow-up time converges to the real blow-up time when the mesh size goes to zero. Numerical experiments are analyzed.
PAMM, 2005
Paper deals with the construction of a priori estimates for the solution of Cauchy problem for an... more Paper deals with the construction of a priori estimates for the solution of Cauchy problem for an abstract linear differential equation in Hilbert space under perturbations of the initial condition, right‐hand side, and operators of the problem. It is shown that a priori estimates of strong stability can be obtained directly on the basis of various a priori estimates for the solution of the Cauchy problem. The perturbations of the operators of the problem are estimated in the corresponding operator norms. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Mathematics of Computation, 1985
Springer Optimization and Its Applications, 2010
In this paper we investigate an initial boundary value problem for a one-dimensional hyperbolic e... more In this paper we investigate an initial boundary value problem for a one-dimensional hyperbolic equation in two disjoint intervals. A finite difference scheme approximating this initial boundary value problem is proposed and analyzed. An estimate of the convergence rate is obtained.
Numerische Mathematik, 1989
SummaryWe study the convergence of the finite-difference schemes for the first initial-boundary v... more SummaryWe study the convergence of the finite-difference schemes for the first initial-boundary value problem for linear second-order parabolic equations with variable coefficients. Using the bilinear version of the Bramble-Hilbert lemma we obtain estimate of convergence, in discreteW21, 1/2 norm, compatible with the smoothness of generalized solutionu∈W2λ, λ/2 (Q) (1