Radiative cooling in glass manufacturing is simulated using the partition of unity finite element method. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary simplified P1 approximation for the radiation in non-grey semitransparent media. To integrate the coupled equations in time we consider a linearly implicit scheme in the finit...

We derive a posteriori error estimates for two classes of explicit finite difference schemes for ordinary differential equations. To facilitate the analysis, we derive a systematic reformulation of the finite difference schemes as finite element methods. The a posteriori error estimates quantify various sources of discretization errors, including effects arising from explicit discretization. Th...

Many numerical methods have been developed for the solution of Poisson and Laplace equations such as finite-difference methods, finite-element methods, boundary-element methods, etc. Sinc numerical methods developed recently by Stenger and co-workers excel over other methods for problems involving singularities, infinite or semi-infinite domains as well as boundary layer behaviors. In this pape...

In this paper we define a finite difference method for the nonstationary 1D flow of the compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamical sense perfect and polytropic. The homogeneous boundary conditions for velocity, microrotation and heat flux are proposed. The sequence of approximate solutions for our problem is constructed by using the def...

In this paper, we present numerical procedures to compute solutions of partial differential equations posed on fractals. particular, consider the strong form equation using standard graph Laplacian matrices and also weak forms derived length or área measure a discrete approximation fractal set. We then introduce procedure normalize obtained diffusions, that is, way renormalization constant need...

II. Foundations 5 A. The Mathematical Structure of Physical Field Theories . . . 5 B. Geometric Objects and Orientation . . . . . . . . . . . . . 7 C. Physical Laws and Physical Quantities . . . . . . . . . . . . 15 D. Classification of Physical Quantities . . . . . . . . . . . . . 21 E. Topological Laws . . . . . . . . . . . . . . . . . . . . . . . 26 F. Constitutive Relations . . . . . . . . ...