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A special two-sided condition for the incremental magnetic reluctivity is introduced which guarantees the unique existence of both the weak and the approximate solutions of the nonlinear stationary magnetic field distributed on a region composed of different media, as well as a certain estimate of the error between the two solutions. The condition, being discussed from the physical as well as the mathematical point of view, can be easily verified and is fulfilled for various magnetic reluctivity...
A simple explicit numerical scheme is proposed for the solution of the Gardner–Ostrovsky
equation (ut + cux + α uux + α1u2ux + βuxxx)x = γu
which is also known as the extended rotation-modified Korteweg–de Vries
(KdV) equation. This equation is used for the description of internal oceanic waves
affected by Earth’ rotation. Particular versions of this equation with zero some of
coefficients, α, α1, β, or
γ are also known in numerous applications....
Si discretizza il problema dell'ostacolo parabolico con differenze all'indietro nel tempo ed elementi finiti lineari nello spazio e si dimostrano stime dell'errore per la frontiera libera discreta.
The solvability of time-harmonic Maxwell equations in the 3D-case with nonhomogeneous conductivities is considered by adapting Sobolev space technique and variational formulation of the problem in question. Moreover, a finite element approximation is presented in the 3D-case together with an error estimate in the energy norm. Some remarks are given to the 2D-problem arising from geophysics.
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