We present a method for computing the dimension of C 1 piecewise polynomials on a triangulated polygonal domain in the plane. Our results verify a conjecture of Strang in a large number of cases. For fourth{degree piecewise polynomials we deene, inductively, a nodal basis on quite general meshes.

We present a stabilized finite element method for Stokes equations with piecewise continuous bilinear approximations for both velocity and pressure variables. The velocity field is enriched with piecewise polynomial bubble functions with null average at element edges. These functions are statically condensed at the element level and therefore they can be viewed as a continuous Q1–Q1 stabilized ...

Abstract. In this paper we present a hybrid finite difference scheme on a piecewise uniform mesh for a class of Black-Scholes equations governing option pricing which is path-dependent. In spatial discretization a hybrid finite difference scheme combining a central difference method with an upwind difference method on a piecewise uniform mesh is used. For the time discretization, we use an impl...

We apply a piecewise constant level set method to elliptic inverse problems. The discontinuity of the coefficients is represented implicitly by a piecewise constant level set function, which allows to use one level set function to represent multiple phases. The inverse problem is solved using a variational penalization method with the total variation regularization of the coefficients. An opera...

We use a front tracking algorithm to explicitly construct entropy solutions for the LighthillWhitham-Richards traffic flow model with a flow-density relationship that is piecewise quadratic, continuous, non-smooth, and non-concave. The solution is exact if the initial condition is piecewise linear and the boundary conditions are piecewise constant. The algorithm serves as a fast and accurate so...

This paper deals with a statistical model fitting procedure for non-stationary time series. This procedure selects the parameters of a piecewise autoregressive model using the Minimum Description Length principle. The existing chromosome representation of the piecewise autoregressive model and its corresponding optimisation algorithm are improved. First, we show that our proposed chromosome rep...