Using the abstract framework of [9] we analyze a residual a posteriori error estimator for space-time finite element discretizations of quasilinear parabolic pdes. The estimator gives global upper and local lower bounds on the error of the numerical solution. The finite element discretizations in particular cover the so-called θ-scheme, which includes the implicit and explicit Euler methods and...

A linear dispersive mechanism for error focusing in polychromatic solutions is identified. This local error pile-up corresponds to the existence of spurious caustics, which are allowed by the dispersive nature of the numerical error. ¿From the mathematical point of view, spurious caustics are related to extrema of the numerical group velocity. Several popular schemes are analyzed and are shown ...

A new theoretical model based on the local composition concept (TNRF-mNRTL model) was proposed to express the short-range contribution of the excess Gibbs energy for the solutions containing polymer and electrolyte. This contribution of interaction along with the long-range contribution of interaction (Pitzer-Debye-Hückel equation), configurational entropy of mixing (Flory-Huggins relation)...

Background: Energy expenditure is of paramount importance in the assessment of usefulness of wheelchair for paraplegics. Despite widespread recognition of problems associated with currently available mobility systems for persons with spinal cord injuries, development of more efficient systems has been slow.  Lack of a suitable and simple technique for the assessment of energy expenditure in par...

The aim of this project is to solve the Maxwell’s Equation using finite difference (FD) method. We test governing equation by discretizing in 1-Dimensional System describe distribution magnitude Electric and Magnetic Field within subsurface layer. assume that earth layer has constant conductivity (σ) where σ>>εω as a consequence system homogenous isotropic. consider field described diffus...

Previous studies have sought to improve cycling performance by altering various aspects of the pedaling motion using novel crank-pedal mechanisms and non-circular chainrings. However, most designs have been based on empirical data and very few have provided significant improvements in cycling performance. The purpose of this study was to use a theoretical framework that included a detailed musc...

Abstract. We derive optimal order a posteriori error estimates for time discretizations by both the Crank–Nicolson and the Crank–Nicolson–Galerkin methods for linear and nonlinear parabolic equations. We examine both smooth and rough initial data. Our basic tool for deriving a posteriori estimates are second order Crank–Nicolson reconstructions of the piecewise linear approximate solutions. The...

An efficient and accurate numerical scheme is proposed, analyzed and implemented for the Kawahara and modified Kawahara equations which model many physical phenomena such as gravity-capillary waves and magneto-sound propagation in plasmas. The scheme consists of dual-Petrov-Galerkin method in space and Crank-Nicholson-leap-frog in time such that at each time step only a sparse banded linear sys...

The Crank–Nicolson method can be used to solve the Black–Scholes partial differential equation in one-dimension when both accuracy and stability is of concern. In multi-dimensions, however, discretizing the computational grid with a Crank–Nicolson scheme requires significantly large storage compared to the widely adopted Operator Splitting Method (OSM). We found that symmetrizing the system of ...

The spark timing plays a significant role in the combustion process and in deciding the engine parameters of SI engine. This paper aims at demonstrating the effect of advanced and retarded spark timing on the burn fraction variation versus crank angle, cumulative heat release rate versus the crank angle and the pressure variation as a function of crank angle with the help of MATLAB programs. Fo...