1. Lax Equivalence Theorem 1 2. Abstract error analysis 2 3. Application: Finite Difference Method 3 4. Application: Finite Element Method 4 5. Application: Conforming Discretization of Variational Problems 5 6. Application: Perturbed Discretization 6 7. Application: Nonconforming Finite Element Methods 8 8. Application: Finite Volume Method 8 9. Application: Superconvergence of linear finite e...

1. Lax equivalence theorem 1 2. Abstract error analysis 2 3. Application: Finite difference method 3 4. Application: Finite element method 4 5. Application: Conforming Discretization of Variational Problems 5 6. Application: Perturbed Discretization 6 7. Application: Nonconforming finite element methods 7 8. Application: Finite volume method 7 9. Application: Superconvergence of linear finite e...

The time discretization of a very high-order finite volume method may give rise to new numerical difficulties resulting into accuracy degradations. Indeed, for the simple onedimensional unstationary convection-diffusion equation for instance, a conflicting situation between the source term time discretization and the boundary conditions may arise when using the standard Runge-Kutta method. We p...

1 Linear Equation Systems in the Numerical Solution of PDE’s 3 1.1 Examples of PDE’s . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Weak Formulation of Poisson’s Equation . . . . . . . . . . . . 6 1.3 Finite-Difference-Discretization of Poisson’s Equation . . . . . 7 1.4 FD Discretization for Convection-Diffusion . . . . . . . . . . 8 1.5 Irreducible and Diagonal Dominant Matrices . . . ...

The stochastic differential equations for affine jump diffusion models do not yield exact solutions that can be directly simulated. Discretization methods can be used for simulating security prices under these models. However, discretization introduces bias into the simulation results and a large number of time steps may be needed to reduce the discretization bias to an acceptable level. In thi...

This study attempts to identify the merits of six of the most popular discretization methods when confronted with a randomly generated dataset consisting of attributes that conform to one of eight common statistical distributions. It is hoped that the analysis will enlighten as to a heuristic which identifies the most appropriate discretization method to be applied, given some preliminary analy...

Page 2 of 46 Abstract The area of Knowledge discovery and Data mining is growing rapidly. A large number of methods is employed to mine knowledge. Several of the methods rely of discrete data. However, most datasets used in real application have attributes with continuously values. To make the data mining techniques useful for such datasets, discretization is performed as a preprocessing step o...

In this paper, we consider reinitializing level functions through equation /tþ sgnð/Þðkr/k 1Þ 1⁄4 0 [16]. The method of Russo and Smereka [11] is taken in the spatial discretization of the equation. The spatial discretization is, simply speaking, the second order ENO finite difference with subcell resolution near the interface. Our main interest is on the temporal discretization of the equation...

We investigate the discretization of optimal boundary control problems for elliptic equations by the boundary concentrated finite element method. We prove that the discretization error ‖u−uh‖L2(Γ) decreases like N−1, where N is the total number of unknowns. This makes the proposed method favorable in comparison to the h-version of the finite element method, where the discretization error behave...

a two dimensional finite difference lattice boltzmann method (fdlbm) for computing single phase flow problems is developed here. temporal term is discretized with low dissipation-low dispersion. discretization of convective term is implemented with third order upwind method. it will be explained governing equations and numerical method. methodology of imposing boundary conditions in fdlbm is de...