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In this paper we derive a posteriori error estimates for the
heat equation. The time discretization
strategy is based on a θ-method and the mesh used for each
time-slab is independent of the mesh used for the previous
time-slab. The novelty of this paper is an upper bound for the
error caused by the coarsening of the mesh used for computing the
solution in the previous time-slab. The technique applied for
deriving this upper bound is independent of the problem and can be
generalized to other time...
In order to accommodate solutions with multiple
phases, corresponding to crossing rays, we
formulate geometrical optics for the scalar wave equation as
a kinetic transport equation set in phase space.
If the maximum number of phases is finite and known a priori we
can recover the exact multiphase solution from an
associated system of moment equations, closed by an assumption
on the form of the density function in the kinetic equation.
We consider two different closure assumptions based on
delta...
There are many methods and approaches to solving convection--diffusion problems. For those who want to solve such problems the situation is very confusing and it is very difficult to choose the right method. The aim of this short overview is to provide basic guidelines and to mention the common features of different methods. We place particular emphasis on the concept of linear and non-linear stabilization and its implementation within different approaches.
In this article we discuss some issues related to Air Pollution modelling (as viewed by the authors): subgrid parametrization, multiphase modelling, reduction of high dimensional models and data assimilation. Numerical applications are given with POLAIR, a 3D numerical platform devoted to modelling of atmospheric trace species.
We show stability and consistency of the linear semi-implicit complementary volume numerical scheme for solving the regularized, in the sense of Evans and Spruck, mean curvature flow equation in the level set formulation. The numerical method is based on the finite volume methodology using the so-called complementary volumes to a finite element triangulation. The scheme gives the solution in an efficient and unconditionally stable way.
We consider a generalized 1-D von Foerster equation. We present two discretization methods for the initial value problem and study stability of finite difference schemes on regular meshes.
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