In this paper we first modify a widely used discrete Laplace Beltrami operator proposed by Meyer et al over triangular surfaces, and then establish some convergence results for the modified discrete Laplace Beltrami operator over the triangulated spheres. A sequence of spherical triangulations which is optimal in certain sense and leads to smaller truncation error of the discrete Laplace Beltra...

This paper presents a study of a class of PECE algorithms consisting of an application of a predictor followed by application of one iteration of a pseudo NewtonRaphson method to a corrector. Such algorithms require precisely two evaluations of the derivative function for each forward step. Theorems 1 and 4 show that the stability properties of such algorithms compare favorably with those obtai...

Abstract. Second-order boundary value problems are solved with exponentially-fltted Numerov methods. In order to attribute a value to the free parameter in such a method, we look at the leading term of the local truncation error. By solving the problem in two phases, a value for this parameter can be found such that the tuned method behaves like a sixth order method. Furthermore, guidelines to ...

The objective of this project was the analysis and the control of local truncation errors in large eddy simulations. We show that physical reasoning can be incorporated into the design of discretization schemes. Using systematic procedures, a non-linear discretization method is developed where numerical and turbulence-theoretical modeling are fully merged. The truncation error itself functions ...

We propose a fully conservative Front Tracking algorithm in two space dimension. The algorithm rst uses the point shifted algorithm 12] on two adjacent time levels and then constructs space time hexahedra as computational units. We develope and prove a successful geometric construction under certain interface requirement. This algorithm has a rst order local truncation error for cells near the ...

We have learned that the numerical solution obtained from Euler's method, converges to the exact solution () of the initial value problem ′ = (,), (0) = 0 , as ℎ → 0. We now analyze the convergence of a general one-step method of the form +1 = + ℎΦ(, , ℎ), for some continuous function Φ(, , ℎ). We define the local truncation error of this one-step method by (ℎ) = (+1) − () ℎ − Φ(, (), ℎ). That ...