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 $L^2$ 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