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Due to their algorithmic simplicity and high accuracy, force-based model coupling techniques are popular tools in computational physics. For example, the force-based quasicontinuum (QCF) approximation is the only known pointwise consistent quasicontinuum approximation for coupling a general atomistic model with a finite element continuum model. In this… (More)

- Christoph Ortner, Endre Süli
- SIAM J. Numerical Analysis
- 2007

We develop the convergence analysis of discontinuous Galerkin finite element approximations to second-order quasilinear elliptic and hyperbolic systems of partial differential equations of the form, respectively, − ∑d α=1 ∂xαSiα(∇u(x)) = fi(x), i = 1, . . . , d, and ∂2 t ui− ∑d α=1 ∂xαSiα(∇u(t, x)) = fi(t, x), i = 1, . . . , d, with ∂xα = ∂/∂xα, in a… (More)

Abstract. The quasicontinuum method is a coarse-graining technique for reducing the complexity of atomistic simulations in a static and quasistatic setting. In this paper we aim to give a detailed a priori and a posteriori error analysis for a quasicontinuum method in one dimension. We consider atomistic models with Lennard–Jones type long-range… (More)

We consider the propagation of a crack in a brittle material along a prescribed crack path and define a quasi-static evolution by means of stationary points of the free energy. We show that this evolution satisfies Griffith’s criterion in a suitable form which takes into account both stable and unstable propagation, as well as an energy balance formula… (More)

- Siobhan Burke, Christoph Ortner, Endre Süli
- SIAM J. Numerical Analysis
- 2010

Abstract. The energy of the Francfort–Marigo model of brittle fracture can be approximated, in the sense of Γ-convergence, by the Ambrosio–Tortorelli functional. In this work we formulate and analyze two adaptive finite element algorithms for the computation of its (local) minimizers. For each algorithm we combine a Newton-type method with residual-driven… (More)

A sharp stability analysis of atomistic-to-continuum coupling methods is essential for evaluating their capabilities for predicting the formation and motion of lattice defects. We formulate a simple one-dimensional model problem and give a detailed analysis of the stability of the force-based quasicontinuum (QCF) method. The focus of the analysis is the… (More)

- Christoph Ortner
- Math. Comput.
- 2011

For a next-nearest neighbour pair interaction model in a periodic domain, a priori and a posteriori analyses of the quasinonlocal quasicontinuum method (QNL-QC) are presented. The results are valid for large deformations and essentially guarantee a one-to-one correspondence between atomistic solutions and QNL-QC solutions. The analysis is based on… (More)

- M Schuster, E Wasserbauer, +4 authors G Werner
- Journal of biomolecular screening
- 2000

Identification of new target proteins is a novel paradigm in drug discovery. A major bottleneck of this strategy is the rapid and simultaneous expression of proteins from differential gene expression to identify eligible candidates. By searching for a generic system enabling high throughput expression analysis and purification of unknown cDNAs, we evaluated… (More)

- Christian Nischler, Hannes Oberkofler, +5 authors Stefan F Egger
- Acta ophthalmologica
- 2011

PURPOSE
To determine whether different complement factor H (CFH) genotypes play a role in treatment of age-related macular degeneration (AMD) with intravitreal bevacizumab.
METHODS
In this prospective study, we included 197 patients with exudative AMD and treated with 1.25 mg intravitreal bevacizumab at 6-week intervals until choroidal neovascularization… (More)

In this paper we present several extensions of theoretical tools for the analysis of Discontinuous Galerkin (DG) method beyond the linear case. We define broken Sobolev spaces for Sobolev indices in [1,∞), and we prove generalizations of many techniques of classical analysis in Sobolev spaces. Our targeted application is the convergence analysis for DG… (More)