finite and boundary element methods have been used by many authors to solve mathematicalphysics problems. however, the coupling of these two methods happens to be more efficient as it combinestheir merits. in this paper, the mathematical analysis of the coupling of finite and boundary element methodsfor the helmholtz equation is presented.

‎semidiscrete finite element approximation of a hyperbolic type‎ ‎integro-differential equation is studied. the model problem is‎ ‎treated as the wave equation which is perturbed with a memory term.‎ ‎stability estimates are obtained for a slightly more general problem.‎ ‎these, based on energy method, are used to prove optimal order‎ ‎a priori error estimates.‎

We develop an improved lattice-Boltzmann numerical scheme to solve magnetohydrodynamic (MHD) equations in the regime of low magnetic Reynolds numbers, grounded on central-moment (CM) and multi-relaxation-time (MRT) collision models. The simulation induction equation within approach MHD has been usually devised along lines simplest phenomenological description—the single relaxation time (SRT) mo...

Continuing research in [13] and [14] on well-posedness of the optimal time control problem with a constant convex dynamics (in a Hilbert space), we adapt one of the regularity conditions obtained there to a slightly more general problem, where nonaffine additive term appears. We prove existence and uniqueness of a minimizer in this problem as well as continuous differentiability of the value fu...

Theorem 3.2 in the paper is incorrect since the left-hand side of equation (15) in [2] is multiplicative while the right-hand side is not. Therefore, Theorem 5.2 and Table 1, which use the result of Theorem 3.2, are wrong. However, the description of a Siegel lattice (Theorem 4.4) is correct. From the description of a Siegel lattice, using the methods in [1], we can compute the values of ζK(−1)...

In elementary mathematics, the simplest variety – i.e., geometric object defined by polynomial equations – that one encounters is a line, i.e., the set of points in the Euclidean plane R defined by an equation of the form aX + bY = c (where a, b, c ∈ R). After translation, rotation, and dilation, such an equation may be written in the form X = 0. In this case, the variety in question passes thr...