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A free boundary stationary magnetohydrodynamic problem in connection with the electromagnetic casting process

100%
Roliński T.
Annales Polonici Mathematici
|
1995
|
tom 61
|
nr 3
195-223
EN
We investigate the behaviour of the meniscus of a drop of liquid aluminium in the neighbourhood of a state of equilibrium under the influence of weak electromagnetic forces. The mathematical model comprises both Maxwell and Navier-Stokes equations in 2D. The meniscus is governed by the Young-Laplace equation, the data being the jump of the normal stress. To show the existence and uniqueness of the solution we use the classical implicit function theorem. Moreover, the differentiability of the operator solving this problem is established.
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A method for solving the Neumann problem for the Poisson equation on the exterior of a poligon

100%
Roliński T.
Mathematica Applicanda
|
1993
|
tom 22
|
nr 36
PL
.
EN
This paper is concerned with a numerical method for solving the problem Δu=f in Ωc (=intR2\Ω), (du/dn)|Γ=g, where ΩR2 is a polygon and Γ is the boundary of Ω. The method is based on coupling finite and boundary element techniques. To compensate for the loss of smoothness of the solution u near the corners of the polygon Ω we refine the triangulation without changing the number of triangles. We apply the affine triangular Lagrangean element of degree kN and the Lagrangean boundary element of degree k−1 to obtain the optimal order of convergence via the Galerkin projection.
3
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An analysis of the exterior Neumann problem for the Poisson equation in connection with a numerical procedure

100%
Roliński T.
Mathematica Applicanda
|
1993
|
tom 22
|
nr 36
PL
.
EN
This paper is concerned with transforming the exterior problem Δu=f on Ωc, (∂u/∂n)|Γ=g, where ΩR2 is a bounded region and Ω^(c)=int(R2\Ω), into a problem represented by two equations. The first one is posed on a bounded domain and the second one is posed on the outer part of the boundary of the domain. This new problem is suitable for a numerical method based on coupling the finite and boundary element methods.
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