100 research outputs found
A priori and a posteriori error estimates for the quad-curl eigenvalue problem
In this paper, we consider a priori and a posteriori error estimates of the H(curl2)-conforming finite element when solving the quad-curl eigenvalue problem. An a priori estimate of eigenvalues with convergence order 2(s − 1) is obtained if the corresponding eigenvector u ∈ Hs − 1(Ω) and ∇ × u ∈ Hs(Ω). For the a posteriori estimate, by analyzing the associated source problem, we obtain lower and upper bounds for the errors of eigenvectors in the energy norm and upper bounds for the errors of eigenvalues. Numerical examples are presented for validation
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Computational Engineering
This Workshop treated a variety of finite element methods and applications in computational engineering and expanded their mathematical foundation in engineering analysis. Among the 53 participants were mathematicians and engineers with focus on mixed and nonstandard finite element schemes and their applications
An arbitrary-order discrete rot-rot complex on polygonal meshes with application to a quad-rot problem
In this work, following the discrete de Rham (DDR) approach, we develop a
discrete counterpart of a two-dimensional de Rham complex with enhanced
regularity. The proposed construction supports general polygonal meshes and
arbitrary approximation orders. We establish exactness on a contractible domain
for both the versions of the complex with and without boundary conditions and,
for the former, prove a complete set of Poincar\'e-type inequalities. The
discrete complex is then used to derive a novel discretisation method for a
quad-rot problem which, unlike other schemes in the literature, does not
require the forcing term to be prepared. We carry out complete stability and
convergence analyses for the proposed scheme and provide numerical validation
of the results
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Mini-Workshop: Efficient and Robust Approximation of the Helmholtz Equation
The accurate and efficient treatment of wave propogation phenomena is still a challenging problem. A prototypical equation is the Helmholtz equation at high wavenumbers. For this equation, Babuška & Sauter showed in 2000 in their seminal SIAM Review paper that standard discretizations must fail in the sense that the ratio of true error and best approximation error has to grow with the frequency. This has spurred the development of alternative, non-standard discretization techniques. This workshop focused on evaluating and comparing these different approaches also with a view to their applicability to more general wave propagation problems
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Schnelle Löser für partielle Differentialgleichungen
The workshop Schnelle Löser für partielle Differentialgleichungen, organised by Randolph E. Bank (La Jolla), Wolfgang Hackbusch(Leipzig), Gabriel Wittum (Heidelberg) was held May 22nd - May 28th, 2005. This meeting was well attended by 47 participants with broad geographic representation from 9 countries and 3 continents. This workshop was a nice blend of researchers with various backgrounds
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Computational Electromagnetism and Acoustics
The challenge inherent in the accurate and efficient numerical modeling of wave propagation phenomena is the common grand theme in both computational electromagnetics and acoustics. Many excellent contributions at this Oberwolfach workshop were devoted to this theme and a wide range of numerical techniques and algorithms were mustered to tackle this challenge
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Gemischte und nicht-standard Finite-Elemente-Methoden mit Anwendungen
Mixed and non-conforming finite element methods form a general mathematical framework for the spatial discretisation of partial differential equations, mainly applied to elliptic equations of second order and are becoming increasingly important for the solution of nonlinear problems. These methods are under active discussion in the mathematical and the engineering community and aim of the workshop was to provide a joint forum for the current state of research
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