In this paper we propose a binary field variant of the Joux-Lercier medium-sized Function Field Sieve, which results not only in complexities as low as Lqn(1/3, 2/3) for computing arbitrary logarithms, but also in an heuristic polynomial time algorithm for finding the discrete logarithms of degree one elements. To illustrate the efficiency of the method, we have successfully solved the DLP in t...

In this note we consider residual-based a posteriori error estimation for finite element approximations of the transport equation. For the discretization we use piecewise affine continuous or discontinuous finite elements and symmetric stabilization of interior penalty type. The lowest order discontinuous Galerkin method using piecewise constant approximation is included as a special case. The ...

We present a numerical method for the computat ion of discrete solutions of the Plateau Problem. This problem consists of the investigation of minimal surfaces bounded by a prescribed Jordan curve in space. The numerical method allows to compute unstable minimal surfaces with prescribed boundary . It is based on a Boundary Element Method for which asymptotic convergence was proved and which use...

We study the Rayleigh-Stokes problem for a generalized second-grade fluid which involves a Riemann-Liouville fractional derivative in time, and present an analysis of the problem in the continuous, space semidiscrete and fully discrete formulations. We establish the Sobolev regularity of the homogeneous problem for both smooth and nonsmooth initial data [Formula: see text], including [Formula: ...

We present a method of incorporating the discrete dipole approximation (DDA) method with the point matching method to formulate the T -matrix for modeling arbitrarily shaped micro-sized objects. The T -matrix elements are calculated using point matching between fields calculated using vector spherical wave functions and DDA. When applied to microrotors, their discrete rotational and mirror symm...