Review: Ph. G. Ciarlet; The finite element method for elliptic problems
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Effective difference schemes for the heat equation in arbitrary regions
In this paper the author considers the problem of the heat equation ∂u/∂t−(∂2u/∂x21+∂2u/∂x22)=f(x,t) for x∈Ω and t∈(0,T], u(x,0)=φ(x) for x∈Ω, u(x,t)=0 for x∈∂Ω and t∈[0,T]. He constructs a Crank-Nicolson and an alternating direction difference scheme on a regular mesh with steps hi (i=1,2) and τ. Linear interpolation is used for the approximation of the boundary condition. Besides stability of both schemes error estimates are derived under the condition that the derivatives ∂5u/∂t∂x4i and ∂3u/∂t3...
To the members of the Commission of Applied Mathematics of the Committee of Mathematics of the Polsh Academy of Sciences
The author, the Commission Chair, makes a short report on the activity of the Commission in the last year. He pays a special attention to the last meeting of the Commission held in September, 2010 in Zakopane during the XXXIX-th Conference of Applied Mathematics. Two next contributions in this issue of Professors W.~Okrasiński and A.~Jakubowska are written forms of invited presentations to this meeting.
Discussion on the development of applied mathematics in Poland
In 2012. the Commission of Applied Mathematics (CAM) of the Committee of Mathematics Polish Academy of Sciences (CM PAS), which I have the honor to preside in the current term, started a discussion on the development of applied mathematics in Poland. Started this discussion took place in an open meeting of CAM, which took place on the first day of the Conference of Applied Mathematics in Zakopane (4 - 11 September 2012), organized by prof. Łukasz Stettner.
On Jeffreys model of heat conduction
The Jeffreys model of heat conduction is a system of two partial differential equations of mixed hyperbolic and parabolic character. The analysis of an initial-boundary value problem for this system is given. Existence and uniqueness of a weak solution of the problem under very weak regularity assumptions on the data is proved. A finite difference approximation of this problem is discussed as well. Stability and convergence of the discrete problem are proved.
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