Browsing by Author "Sändig, Anna-Margarete"

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Open Access
Coefficient formulae for asymptotic expansions of solutions of elliptic boundary value problems near conical points
(1991) Sändig, Anna-Margarete
It is well known that singularities are present in solutions of elliptic boundary value problems in domains with conical boundary points. The solution consists of singular terms, which appear in a neighbourhood of a conical point, and a more regular term. The coefficients of the singular terms, the so-called stress intensity factors, are especially of interest for applications. We describe a method, how some of them may be calculated, if the right hand sides are from standard Sobolev spaces. In some cases the coefficients are unstable and a stabilization procedure is necessary.We handle as examples boundary value problems for the Laplace equation in two and three dimensional domains.
Open Access
Error estimates for finite-element solutions of elliptic boundary value problems in non-smooth domains
(1990) Sändig, Anna-Margarete
Es werden Fehlerabschätzungen in verschiedenen Normen (nämlich in W m,2(Ω) und L p(Ω), 2≤p≤∞) von standarden Finite-Elemente-Lösungen von elliptischen Randwertproblemen in beschränkten Gebieten im R n mit konischen Punkten oder nichtüberschneidenden Punkten oder nichtüberschneidenden Kanten betrachtet.
Open Access
General interface problems. 1
(1994) Nicaise, Serge; Sändig, Anna-Margarete
We study transmission problems for elliptic operators of order 2m with general boundary and interface conditions, introducing new covering conditions. This allows to prove solvability, regularity and asymptotics of solutions in weighted Sobolev spaces. We give some numerical examples for the location of the singular exponents.
Open Access
General interface problems. 2
(1994) Nicaise, Serge; Sändig, Anna-Margarete
We study transmission problems for elliptic operators of order 2m with general boundary and interface conditions, introducing new covering conditions. This allows to prove solvability, regularity and asymptotics of solutions in weighted Sobolev spaces. We give some numerical examples for the location of the singular exponents.
Open Access
The regularity of boundary value problems for the Lamé equations in a polygonal domain
(1989) Sändig, Anna-Margarete; Richter, Uwe; Sändig, Rainer
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Open Access
Singularities of non-rotationally symmetric solutions of boundary value problems for the Lamé equations in a 3 dimensional domain with conical points
(1992) Sändig, Anna-Margarete; Sändig, Rainer
It is well known that singularities are present in solutions of boundary value problems for the Lamé equations in conical domains. It follows from the general theory that the solutions consist of singular terms of the form r α (ln r) q F(α, φ, θ) (r is the distance to the vertex of the cone φ, and θ are the spherical angles) and α more regular term. Rotationally symmetric solutions of the Lamé equations under zero boundary displacements or stress free boundary conditions are investigated in (1, 2), where the values of α and q have been computed. Here we are concerned with the more general case, namely that the volume and surface forces of our problems are non rotationally symmetric. That means that the solutions depend not only on r and θ, but on the polar angle φ too. Using a monotonicity principle of Kozlov, Maz'ja und Schwab one can get regularity results for polyhedral domains too.
Open Access
Singularities of rotationally symmetric solutions of boundary value problems for the Lamé equations
(1991) Beagles, Adam Edward; Sändig, Anna-Margarete
We apply the theory of elliptic boundary value problems in non-smooth domains with conical points to rotationally symmetric solutions of boundary value problems for the Lamé equations. The resulting expansion involves singular vector-functions which, in turn, depend on a parameter, α. We here present equations which determine the values of α for either stress-free or Dirichlet boundary conditions. We give a numerical algorithm whereby α can be computed and present some plots of the values obtained. The singular vector-functions are given explicitly and we present equations for the computation of the coefficients of the expansion.