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We consider elliptic problems with complicated, discontinuous diffusion tensor $A_{\scriptscriptstyle 0} $. One of the standard approaches to numerically treat such problems is to simplify the coefficient by some approximation, say $A_{\varepsilon}$, and to use standard finite elements. In \cite{Repin2012} a combined modelling-discretization strategy has been proposed which estimates the discretization and modelling errors by a posteriori estimates of functional type. This strategy allows to balance these two errors in a problem adapted way. However, the estimate of the modelling error is derived under the assumption that the difference $A_{\scriptscriptstyle 0} -A_{\varepsilon}$ is bounded in the $L^{\infty}$-norm, which requires that the approximation of the coefficient matches the discontinuities of the original coefficient. Therefore this theory is not appropriate for applications with discontinuous coefficients along \textit{complicated, curved} interfaces. Based on bounds for $A_{\scriptscriptstyle 0} -A_{\varepsilon}$ in an $L^{q}$-norm with $q

In this paper, we will introduce composite finite elements for solving elliptic boundary value problems with discontinuous coefficients. The focus is on problems where the geometry of the interfaces between the smooth regions of the coefficients is very complicated. On the other hand, efficient numerical methods such as, e.g., multigrid methods, wavelets, extrapolation, are based on a multi-scale discretization of the problem. In standard finite element methods, the grids have to resolve the structure of the discontinuous coefficients. Thus, straightforward coarse scale discretizations of problems with complicated coefficient jumps are not obvious. In this paper, we define composite finite elements for problems with discontinuous coefficients. These finite elements allow the coarsening of finite element spaces independently of the structure of the discontinuous coefficients. Thus, the multigrid method can be applied to solve the linear system on the fine scale. We focus on the construction of the composite finite elements and the efficient, hierarchical realization of the intergrid transfer operators. Finally, we present some numerical results for the multigrid method based on the composite finite elements (CFE-MG)

Hintergrund: Das Stigma psychischer Erkrankungen ist ein Hindernis für die Behandlung von Menschen mit psychischen Erkrankungen und steht deren Genesung und sozialen Inklusion im Wege. Neben Ansätzen zur Bekämpfung des Stigmas, die sich an spezielle Zielgruppen wie z. B. Schüler [for full text, please go to the a.m. URL], 12. Deutscher Kongress für Versorgungsforschung

The Minihouse is a prototupe for a sustainable townhouse. On a site of only 29 sqm it offers 154 sqm of urban life. The project 'Minimum Impact House' adresses two important questions: How do we provide living space in the cities without distroying the landscape? How to improve sustainably the ecological, economical and socio-cultural performance of buildings?

The aims of trial NHL-BFM 90 for patients (pts) suffering from B-cell neoplasms are to prove whether: 1. Treatment for pts with complete resection can be reduced from 3 to 2 therapy courses; 2. Results for pts of stage III with large abdominal tumors can be improved by high dose (HD) chemotherapy; 3. Survival for pts with incomplete initial response can be improved by therapy intensification; 4. Intraventricularly applied CNS chemotherapy can improve the outcome for CNS positive pts. Therapy is stratified into 3 branches. Branch 1: completely resected; branch 2: not resected, extra-abdominal localization only or abdominal localization and LDH500 U/l; branch 3: abdominal localization and LDHor = 500 U/l, and all pts with BM or/and CNS involvement or multifocal bone disease. A 5-day prephase is followed by 2 (R1), 4 (R2), 6 (R3) therapy courses composed of dexamethasone (DEXA), methotrexate (MTX) 5 g/m2/24 h (in branch R1, 500 mg/m2), MTX/Cytarabine (ARA-C)/prednisolone (PRED) i.th., vincristine (not in branch R1), ifosfamide alternating with cyclophosphamide, ARA-C/etoposide (VP16) alternating with doxorubicin. CNS pos. pts receive MTX/ARA-C/PRED applied intraventricularly. Pts with incomplete response after 2 courses receive an intensification (DEXA, Vindesine, HD-ARA-C, VP16, and MTX/ARA-C/PRED i.th.). Pts with viable tumor after the intensified course receive mega-dose chemotherapy with autologous BM rescue (aBMT). From 4/1990 to 12/1992, 228 pts were registered; 212 pts are evaluable for response. The probability of event free survival (pEFS) at 3 years is 89 +/- 2% for the whole group, 97 +/- 3% for pts of branch R1 (n = 32), 99 +/- 1% for patients of branch R2 (n = 87), and 77 +/- 4% for patients of branch R3 (n = 94) (median observation time 21 months). 7 pts of branch R3 died early due to infections. 15 pts failed therapy (one pt each in branch R1, and R2, 13 pts in branch R3). pEFS for pts with stage III abdominal disease and LDHor = 500 U/l is 80 +/- 6 as compared to 53 +/- 8% in the preceding studies (p.02). Of 13 evaluable pts with CNS disease 3 died early of infection, however none suffered from relapse. Only 1 of 22 pts of branch R2 who had residual tumors after 2 therapy courses suffered from progress in contrast to 9 of 33 such pts of branch R3. Only 2 pts had viable tumor after the intensification course CC. They received aBMT, both are in CCR.(ABSTRACT TRUNCATED AT 400 WORDS)

It is well known that standard h-version finite element discretisations using lowest order elements for Helmholtz' equation suffer from the following stability condition: 's'sThe mesh width h of the finite element mesh has to satisfy k 2 h≲1'', where k denotes the wave number. This condition rules out the reliable numerical solution of Helmholtz equation in three dimensions for large wave numbers k≳50. In our paper, we will present a refined finite element theory for highly indefinite Helmholtz problems where the stability of the discretisation can be checked through an 's'salmost invariance'' condition. As an application, we will consider a one-dimensional finite element space for the Helmholtz equation and apply our theory to prove stability under the weakened condition hk≲1 and optimal convergence estimates

In this paper we consider the three-dimensional wave equation in unbounded domains with Dirichlet boundary conditions. We start from a retarded single layer potential ansatz for the solution of these equations which leads to the retarded potential integral equation (RPIE) on the bounded surface of the scatterer. We formulate an algorithm for the spacetime Galerkin discretization with smooth and compactly supported temporal basis functions which have been introduced in [S. Sauter and A. Veit: A Galerkin Method for Retarded Boundary Integral Equations with Smooth and Compactly Supported Temporal Basis Functions, Preprint 04-2011, Universitat Zurich]. For the debugging of an implementation and for systematic parameter tests it is essential to have some explicit representations and some analytic properties of the exact solutions for some special cases at hand. We will derive such explicit representations for the case that the scatterer is the unit ball. The obtained formulas are easy to implement and we will present some numerical experiments for these cases to illustrate the convergence behaviour of the proposed method. AMS subject classifications. 35L05, 65R20

In this paper, we consider the numerical discretization of elliptic eigenvalue problems by Finite Element Methods and its solution by a multigrid method. From the general theory of finite element and multigrid methods, it is well known that the asymptotic convergence rates become visible only if the mesh width h is sufficiently small, h ≤ h 0. We investigate the dependence of the maximal mesh width h 0 on various problem parameters such as the size of the eigenvalue and its isolation distance. In a recent paper (Sauter in Finite elements for elliptic eigenvalue problems in the preasymptotic regime. Technical Report. Math. Inst., Univ. Zurich, 2007), the dependence of h 0 on these and other parameters has been investigated theoretically. The main focus of this paper is to perform systematic experimental studies to validate the sharpness of the theoretical estimates and to get more insights in the convergence of the eigenfunctions and -values in the preasymptotic regime.

In this paper, we define a new class of finite elements for the discretization of problems with Dirichlet boundary conditions. In contrast to standard finite elements, the minimal dimension of the approximation space is independent of the domain geometry and this is especially advantageous for problems on domains with complicated micro-structures. For the proposed finite element method we prove the optimal-order approximation (up to logarithmic terms) and convergence estimates valid also in the cases when the exact solution has a reduced regularity due to re-entering corners of the domain boundary. Numerical experiments confirm the theoretical results and show the potential of our proposed method.

In this paper, we will present a new approach for solving boundary integral equations with panel clustering. In contrast to all former versions of panel clustering, the computational and storage complexity of the algorithm scales linearly with respect to the number of degrees of freedom without any additional logarithmic factors. The idea is to develop alternative formulations of all classical boundary integral operators for the Laplace problem where the kernel function has a reduced singular behaviour. It turns out that the application of the panel-clustering method with variable approximation order preserves the asymptotic convergence rate of the discretisation and has significantly reduced complexity.