In this paper we study a model problem describing the movement of
a glacier under Glen's flow law and investigated by Colinge and
Rappaz [Colinge and Rappaz, ESAIM: M2AN33 (1999) 395–406]. We establish error estimates for finite
element approximation using the results of Chow [Chow, SIAM J. Numer. Analysis29 (1992) 769–780] and
Liu and Barrett [Liu and Barrett, SIAM J. Numer. Analysis33
(1996) 98–106] and give an analysis of the
convergence of the successive approximations used in [Colinge and...
The paper presents the solution to the geodetic boundary value problem by the finite element method in area of Slovak Republic. Generally, we have made two numerical experiments. In the first one, Neumann BC in the form of gravity disturbances generated from EGM-96 is used and the solution is verified by the quasigeoidal heights generated directly from EGM-96. In the second one, Neumann BC is computed from gravity measurements and the solution is compared to the quasigeoidal heights obtained by...
Durations of rain events and drought events over a given region provide important information about the water resources of the region. Of particular interest is the shape of upper tails of the probability distributions of such durations. Recent research suggests that the underlying probability distributions of such durations have heavy tails of hyperbolic type, across a wide range of spatial scales from 2 km to 120 km. These findings are based on radar measurements of spatially averaged rain rate...
2000 Mathematics Subject Classification: Primary 26A33; Secondary 35S10, 86A05Fractional diffusion equations are abstract partial differential equations
that involve fractional derivatives in space and time. They are useful to
model anomalous diffusion, where a plume of particles spreads in a different
manner than the classical diffusion equation predicts. An initial value problem
involving a space-fractional diffusion equation is an abstract Cauchy
problem, whose analytic solution can be written...