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Finite element approximation of a contact vector eigenvalue problem

Hennie de Schepper;  Roger Van Keer — 2003

Applications of Mathematics

We consider a nonstandard elliptic eigenvalue problem of second order on a two-component domain consisting of two intervals with a contact point. The interaction between the two domains is expressed through a coupling condition of nonlocal type, more specifically, in integral form. The problem under consideration is first stated in its variational form and next interpreted as a second-order differential eigenvalue problem. The aim is to set up a finite element method for this problem. The error...

Fischer decompositions in Euclidean and Hermitean Clifford analysis

Freddy Brackx;  Hennie de Schepper;  Vladimír Souček — 2010

Archivum Mathematicum

Euclidean Clifford analysis is a higher dimensional function theory studying so–called monogenic functions, i.e. null solutions of the rotation invariant, vector valued, first order Dirac operator ∂ ̲ . In the more recent branch Hermitean Clifford analysis, this rotational invariance has been broken by introducing a complex structure J on Euclidean space and a corresponding second Dirac operator ∂ ̲ J , leading to the system of equations ∂ ̲ f = 0 = ∂ ̲ J f expressing so-called Hermitean monogenicity. The invariance of this...

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