The algorithmic pattern of the hp Discontinuous Galerkin Finite Element Method (DGFEM) for the time semidiscretization of abstract parabolic evolution equations is presented. In combination with a continuous hp discretization in space we obtain a fully discrete hp-scheme for the numerical solution of parabolic problems. Numerical examples for the heat equation in a two dimensional domain confir...

The fact that the time optimal controls for parabolic equations have the bang–bang property has been recently proved for controls distributed inside the considered domain (interior control). The main result in this article asserts that the boundary controls for the heat equation have the same property, at least in rectangular domains. This result is proved by combining methods from traditionall...

an analytical study was performed to study effects of thermo-diffusion and chemical reactions on a three-dimensional mhd mixed convective flow of dissipative fluid along an infinite vertical porous plate with transverse sinusoidal suction velocity. the parabolic partial differential equations governing the fluid flow, heat transfer, and mass transfer were solved using perturbation technique and...

Abstract. An a posteriori error estimate for finite volume methods in triangular meshes is developed and successfully implemented for parabolic heat transfer problems. The proposed error estimate belongs to the class of truncation-error estimates. A polynomial function was successfully employed in the estimation of the solution used in the error formulation. A simple and reliable h-type adaptiv...

We introduce a new family of numerical algorithms for approximating solutions general high-dimensional semilinear parabolic partial differential equations at single space-time points. The algorithm is obtained through delicate combination the Feynman-Kac and Bismut-Elworthy-Li formulas, an approximate decomposition Picard fixed-point iteration with multilevel accuracy. has been tested on variet...

In this paper, we present results of the development certain parallel numerical methods for solving three-dimensional evolutionary and stationary problems diffusion heat transfer. We a detailed description special, explicit iteration scheme parabolic equations discuss multigrid technology used elliptic implicit schemes equations.

A. Local and global Carleman estimates play a central role in the study of some partial differential equations regarding questions such as unique continuation and controllability. We survey and prove such estimates in the case of elliptic and parabolic operators by means of semi-classical microlocal techniques. Optimality results for these estimates and some of their consequences are pre...

The mode of operation of mini parabolic solar panels made of germanium, mild steel and aluminium were investigated experimentally, as means of providing heated water on a farmland; the process was also modelled. Angular adjustments of the solar collectors from 70-90o were adopted in order to determine, the best material of construction for the parabolic solar collector and the angular orientati...