64 research outputs found
Recommended from our members
Error estimates in weighted Sobolev norms for finite element immersed interface methods
When solving elliptic partial differential equations in a region
containing immersed interfaces (possibly evolving in time), it is often
desirable to approximate the problem using a uniform background
discretisation, not aligned with the interface itself. Optimal convergence
rates are possible if the discretisation scheme is enriched by allowing the
discrete solution to have jumps aligned with the surface, at the cost of a
higher complexity in the implementation. A much simpler way to reformulate
immersed interface problems consists in replacing the interface by a singular
force field that produces the desired interface conditions, as done in
immersed boundary methods. These methods are known to have inferior
convergence properties, depending on the global regularity of the solution
across the interface, when compared to enriched methods. In this work we
prove that this detrimental effect on the convergence properties of the
approximate solution is only a local phenomenon, restricted to a small
neighbourhood of the interface. In particular we show that optimal
approximations can be constructed in a natural and inexpensive way, simply by
reformulating the problem in a distributionally consistent way, and by
resorting to weighted norms when computing the global error of the
approximation
Error estimates in weighted Sobolev norms for finite element immersed interface methods
When solving elliptic partial differential equations in a region containing immersed interfaces (possibly evolving in time), it is often desirable to approximate the problem using a uniform background discretisation, not aligned with the interface itself. Optimal convergence rates are possible if the discretisation scheme is enriched by allowing the discrete solution to have jumps aligned with the surface, at the cost of a higher complexity in the implementation. A much simpler way to reformulate immersed interface problems consists in replacing the interface by a singular force field that produces the desired interface conditions, as done in immersed boundary methods. These methods are known to have inferior convergence properties, depending on the global regularity of the solution across the interface, when compared to enriched methods. In this work we prove that this detrimental effect on the convergence properties of the approximate solution is only a local phenomenon, restricted to a small neighbourhood of the interface. In particular we show that optimal approximations can be constructed in a natural and inexpensive way, simply by reformulating the problem in a distributionally consistent way, and by resorting to weighted norms when computing the global error of the approximation
A weighted Hybridizable Discontinuous Galerkin method for drift-diffusion problems
In this work we propose a weighted hybridizable discontinuous Galerkin method
(W-HDG) for drift-diffusion problems. By using specific exponential weights
when computing the product in each cell of the discretization, we are
able to replicate the behavior of the Slotboom change of variables, and
eliminate the drift term from the local matrix contributions. We show that the
proposed numerical scheme is well-posed, and numerically validates that it has
the same properties of classical HDG methods, including optimal convergence,
and superconvergence of postprocessed solutions. For polynomial degree zero,
dimension one, and vanishing HDG stabilization parameter, W-HDG coincides with
the Scharfetter-Gummel stabilized finite volume scheme (i.e., it produces the
same system matrix). The use of local exponential weights generalizes the
Scharfetter-Gummel stabilization (the state-of-the-art for Finite Volume
discretization of transport-dominated problems) to arbitrary high-order
approximations.Comment: 27 pages, 4 figures, 4 table
Error estimates of B-spline based finite-element method for the wind-driven ocean circulation
We present the error analysis of a B-spline based finite-element approximation of the stream-function formulation of the large scale wind-driven ocean circulation. In particular, we derive optimal error estimates for h-refinement using a Nitsche-type variational formulations of the two simplied linear models of the stationary quasigeostrophic equations, namely the Stommel and Stommel--Munk models. Numerical results on rectangular and embedded geometries confirm the error analysis
Generation of induced pluripotent stem cell line, CSSi004-A (2962), from a patient diagnosed with Huntington's disease at the presymptomatic stage
Huntington's disease (HD) is an incurable, autosomal dominant, hereditary neurodegenerative disorder that typically manifests itself in midlife. This pathology is linked to the deregulation of multiple, as yet unknown, cellular processes starting before HD onset. A human iPS cell line was generated from skin fibroblasts of a subject at the presymptomatic life stage, carrying a polyglutamine expansion in HTT gene codifying Huntingtin protein. The iPSC line contained the expected CAG expansion, expressed the expected pluripotency markers, displayed in vivo differentiation potential to the three germ layers and had a normal karyotype
Validation and application of a quantitative real-time PCR assay to detect common wheat adulteration of durum wheat for pasta production
Pasta is the Italian product par excellence and it is now popular worldwide. Pasta of a superior quality is
made with pure durum wheat. In Italy, addition of Triticum aestivum (common wheat) during manufacturing
is not allowed and, without adequate labeling, its presence is considered an adulteration. PCRrelated
techniques can be employed for the detection of common wheat contaminations. In this work,
we demonstrated that a previously published method for the detection of T. aestivum, based on the gliadin
gene, is inadequate. Moreover, a new molecular method, based on DNA extraction from semolina and
real-time PCR determination of T. aestivum in Triticum spp., was validated. This multiplex real-time PCR,
based on the dual-labeled probe strategy, guarantees target detection specificity and sensitivity in a short
period of time. Moreover, the molecular analysis of common wheat contamination in commercial wheat
and flours is described for the first time
Generation of induced pluripotent stem cell line, CSSi002-A (2851), from a patient with juvenile Huntington Disease
Abstract Huntington Disease (HD) is an autosomal dominant disorder characterized by motor, cognitive and behavioral features caused by a CAG expansion in the HTT gene beyond 35 repeats. The juvenile form (JHD) may begin before the age of 20 years and is associated with expanded alleles as long as 60 or more CAG repeats. In this study, induced pluripotent stem cells were generated from skin fibroblasts of a 8-year-old child carrying a large size mutation of 84 CAG repeats in the HTT gene. HD appeared at age 3 with mixed psychiatric (i.e. autistic spectrum disorder) and motor (i.e. dystonia) manifestations
Generation of the induced pluripotent stem cell line CSSi006-A (3681) from a patient affected by advanced-stage Juvenile Onset Huntington's Disease
Abstract Juvenile Onset Huntington's Disease (JOHD) is a rare variant of HD withage of onset ≤20 years, accounting for 3–10% of all HD patients. The rarity occurrence of JOHD cases, who severely progress towards mental and physical disability with atypical clinical manifestations compared to classical HD, are responsible of general lack of knowledge about this variant. We obtained a fully reprogrammed iPS cell line from fibroblasts of a JOHD patient carrying 65 CAG repeats and age at onset at age 15. At the biopsy time, the patient showed an advanced stage after 10 years of disease
- …