Existence and regularity of solutions of a phase field model for solidification with convection of pure materials in two dimensions.
Existence and uniqueness for optimal control of oxygen absorption in aquatic system.
Existence of reaction-diffusion-convection waves in unbounded strips.
Finite amplitude thermal convection with variable gravity.
Finite difference solution of radiation effects on MHD unsteady free-convection flow over vertical plate with variable surface temperature.
Flow of a radiating gas between concentric cylinders
Free convection flow of conducting micropolar fluid with thermal relaxation including heat sources.
Free convection flow of water at past an infinite porous plate with constant suction
Free convective flow of a stratified fluid through a porous medium bounded by a vertical plane.
Gas exhalation and its calculations. I
Generalized Harten formalism and longitudinal variation diminishing schemes for linear advection on arbitrary grids
We study a family of non linear schemes for the numerical solution of linear advection on arbitrary grids in several space dimension. A proof of weak convergence of the family of schemes is given, based on a new Longitudinal Variation Diminishing (LVD) estimate. This estimate is a multidimensional equivalent to the well-known TVD estimate in one dimension. The proof uses a corollary of the Perron-Frobenius theorem applied to a generalized Harten formalism.
Generalized Harten Formalism and Longitudinal Variation Diminishing schemes for Linear Advection on Arbitrary Grids
We study a family of non linear schemes for the numerical solution of linear advection on arbitrary grids in several space dimension. A proof of weak convergence of the family of schemes is given, based on a new Longitudinal Variation Diminishing (LVD) estimate. This estimate is a multidimensional equivalent to the well-known TVD estimate in one dimension. The proof uses a corollary of the Perron-Frobenius theorem applied to a generalized Harten formalism.
Global superconvergence of finite element methods for parabolic inverse problems
In this article we transform a large class of parabolic inverse problems into a nonclassical parabolic equation whose coefficients consist of trace type functionals of the solution and its derivatives subject to some initial and boundary conditions. For this nonclassical problem, we study finite element methods and present an immediate analysis for global superconvergence for these problems, on basis of which we obtain a posteriori error estimators.
Heat transfer between a fluid and a plate: multidimensional Laplace transformation methods.
Homogenization of the transport equation describing convection-diffusion processes in a material with fine periodic structure
In the present contribution we discuss mathematical homogenization and numerical solution of the elliptic problem describing convection-diffusion processes in a material with fine periodic structure. Transport processes such as heat conduction or transport of contaminants through porous media are typically associated with convection-diffusion equations. It is well known that the application of the classical Galerkin finite element method is inappropriate in this case since the discrete solution...
Hydrodynamic effect on the three-dimensional flow past a vertical porous plate.
Implicit for local effects and explicit for nonlocal effects is unconditionally stable.
Instabilities of Diffuse Interfaces
Composition gradients in miscible liquids can create volume forces resulting in various interfacial phenomena. Experimental observations of these phenomena are related to some difficulties because they are transient, sufficiently weak and can be hidden by gravity driven flows. As a consequence, the question about their existence and about adequate mathematical models is not yet completely elucidated. In this work we present some experimental evidences of interfacial phenomena in miscible liquids...
Lagrangian and moving mesh methods for the convection diffusion equation
We propose and analyze a semi Lagrangian method for the convection-diffusion equation. Error estimates for both semi and fully discrete finite element approximations are obtained for convection dominated flows. The estimates are posed in terms of the projections constructed in [Chrysafinos and Walkington, SIAM J. Numer. Anal. 43 (2006) 2478–2499; Chrysafinos and Walkington, SIAM J. Numer. Anal. 44 (2006) 349–366] and the dependence of various constants upon the diffusion parameter is ...
Large time behaviour of solutions to nonhomogeneous diffusion equations
This note is devoted to the study of the long time behaviour of solutions to the heat and the porous medium equations in the presence of an external source term, using entropy methods and self-similar variables. Intermediate asymptotics and convergence results are shown using interpolation inequalities, Gagliardo-Nirenberg-Sobolev inequalities and Csiszár-Kullback type estimates.