We design and analyze an adaptive hp-finite element method (hp-AFEM) in dimensions n = 1, 2. The algorithm consists of iterating two routines: hp-NEARBEST finds a near-best hp-approximation of the current discrete solution and data to a desired accuracy, and REDUCE improves the discrete solution to a finer but comparable accuracy. The former hinges on a recent algorithm by Binev for adaptive hp...

In this paper we generalise results regarding the order of accuracy of finite difference operators on Summation-By-Parts (SBP) form, previously known to hold on uniform grids, to grids with arbitrary point distributions near domain boundaries. We give a definite proof that the order of accuracy in the interior of a diagonal norm based SBP operator must be at least twice that of the boundary ste...

The first and second order of accuracy stable difference schemes for the numerical solution of the mixed problem for the fractional parabolic equation are presented. Stability and almost coercive stability estimates for the solution of these difference schemes are obtained. A procedure of modified Gauss elimination method is used for solving these difference schemes in the case of one-dimension...

In this note we consider the application of the WENO scheme to simulations of steady-state flow in a converging diverging nozzle. We demonstrate the recovery of design accuracy through Gegenbauer postprocessing, despite the degradation of the order of accuracy for the numerical solution of the Euler equations to first-order in regions where the characteristics passed through the shock. We have ...

Biodiesel is a promising non-toxic and biodegradable alternative fuel in transport sector. Of all the biodiesel properties, specific gravity and viscosity are the most significant for the effects they have on the utilization of biodiesel fuels in unmodified engines. This paper presents models, which have been derived from experimental data, for predicting the specific gravity and dynamic viscos...

The Cauchy problem for a semilinear parabolic equation is considered. Under the conditions u(x, t) = X(x)T1(t) + T2(t), ∂u ∂x = 0, it is shown that the problem is equivalent to the system of two ordinary differential equations for which exact difference scheme (EDS) with special Steklov averaging and difference schemes with arbitrary order of accuracy (ADS) are constructed on the moving mesh. T...

In this paper, a speed-up strategy for finite volume WENO schemes is developed for solving hyperbolic conservation laws. It adopts p-adaptive like reconstruction, which automatically adjusts from fifth order WENO reconstruction to first order constant reconstruction when nearly constant solutions are detected by the undivided differences. The corresponding order of accuracy for the solutions is...

“Everything should be modular” is an exalted goal stated by almost every architect – but is it really possible to achieve this goal? In this experience paper, we share our lessons learned across a number of restructuring projects that went modular. We discuss typical business motivations, restructuring efforts starting with good intentions, and reconstruction reality striking back. In retrospec...