A local projection stabilized method for fictitious domains

In this work a local projection stabilization method is proposed to solve a fictitious domain problem. The method adds a suitable fluctuation term to the formulation thus rendering the natural space for the Lagrange multiplier stable. Stability and convergence are proved and these results are illustrated by a numerical experiment.Comment: Submitted Preprin

Stabilised hybrid discontinuous Galerkin methods for the Stokes problem with non-standard boundary conditions

In several studies it has been observed that, when using stabilised $\mathbb{P}_k^{}\times\mathbb{P}_k^{}$ elements for both velocity and pressure, the error for the pressure is smaller, or even of a higher order in some cases, than the one obtained when using inf-sup stable $\mathbb{P}_k^{}\times\mathbb{P}_{k-1}^{}$ (although no formal proof of either of these facts has been given). This increase in polynomial order requires the introduction of stabilising terms, since the finite element pairs used do not stability the inf-sup condition. With this motivation, we apply the stabilisation approach to the hybrid discontinuous Galerkin discretisation for the Stokes problem with non-standard boundary conditions

Stabilization arising from PGEM : a review and further developments

The aim of this paper is twofold. First, we review the recent Petrov-Galerkin enriched method (PGEM) to stabilize numerical solutions of BVP's in primal and mixed forms. Then, we extend such enrichment technique to a mixed singularly perturbed problem, namely, the generalized Stokes problem, and focus on a stabilized finite element method arising in a natural way after performing static condensation. The resulting stabilized method is shown to lead to optimal convergences, and afterward, it is numerically validated

Consistent local projection stabilized finite element methods

This work establishes a formal derivation of local projection stabilized methods as a result of an enriched Petrov-Galerkin strategy for the Stokes problem. Both velocity and pressure finite element spaces are enhanced with solutions of residual-based local problems, and then the static condensation procedure is applied to derive new methods. The approach keeps degrees of freedom unchanged while gives rise to new stable and consistent methods for continuous and discontinuous approximation spaces for the pressure. The resulting methods do not need the use of a macro-element grid structure and are parameter-free. The numerical analysis is carried out showing optimal convergence in natural norms, and moreover, two ways of rendering the velocity field locally mass conservative are proposed. Some numerics validate the theoretical results

Finite element eigenvalue enclosures for the Maxwell operator

We propose employing the extension of the Lehmann-Maehly-Goerisch method developed by Zimmermann and Mertins, as a highly effective tool for the pollution-free finite element computation of the eigenfrequencies of the resonant cavity problem on a bounded region. This method gives complementary bounds for the eigenfrequencies which are adjacent to a given real parameter. We present a concrete numerical scheme which provides certified enclosures in a suitable asymptotic regime. We illustrate the applicability of this scheme by means of some numerical experiments on benchmark data using Lagrange elements and unstructured meshes.Comment: arXiv admin note: substantial text overlap with arXiv:1306.535

La alboka

La alboka es un instrumento pastoril muy antiguo compuesto de dos tubos sonoros de caña con orificios, dos espitas de caña que se acoplan a los tubos, boquilla y pabellón, ambos de cuerno, segmento semicircular de madera. Se intenta dar una explicación al origen y evolución de la alboka, así como el origen de su nombr

Dracula as Inter-American Film Icon: Universal Pictures and Cinematográfica ABSA

My essay explores the vampire cinema of Hollywood and Mexico. In particular, I trace the relationship between Universal Pictures as the progenitor of horror during the Great Depression and Cinematográfica ABSA\u27s mexploitation practices. The latter resulted in the first vampire film in Latin America-- El vampiro (1957). Rather than strengthening separatist national cinemas, the unintended consequences of genre film production make this a case of inter-American scope

Patrimonio, narrativas racializadas y políticas de la memoria. Abordaje a un manuscrito afrodescendiente en el Valle de Azapa / Heritage, racialized narratives and politics of memory. Approach to an afro manuscript from Azapa Valley

El presente artículo es una lectura crítica al dispositivo patrimonio a través del abordaje interdisciplinario a un manuscrito encontrado en el Valle de Azapa (Arica), testimonio de un agricultor afrodescendiente a principios del siglo XX. Las manifestaciones literarias, cartas, décimas y poesías, registradas en el que hemos denominado “Documento Baluarte”, no sólo relevan las experiencias de miles de sujetos/as que fueron marcados/as por la violencia durante el periodo de la chilenización en la zona norte (sur para Perú); sino que, también, supone la necesidad de asumir y construir un locus teórico que incorpore aquellas subjetividades obliteradas por el relato nacional chileno. Tanto objeto como contenido abren una zona de disputa donde es posible problematizar las políticas de la memoria en Chile y, en ello,  una noción de patrimonio monolítica e incontroversial.   Palabras clave: Estudios del patrimonio – Literatura chilena - Estudios culturales Abstract: This article is a critical approach to heritage device through an interdisciplinary approach to a manuscript founded in Azapa Valley (Arica), written by an afro farmer in the early twentieth century. The literary forms, letters, décimas and poetry, captured in what we have called "Document Baluarte", is not only possible to survey the experiences of thousands of subjects they were marked by state violence during the period called “chilenización” in the north of Chile (south to Peru); but also implies to take and build a theoretical field that incorporates those subjectivities silenced by the chilean narrative. Both, book and its contents open an area of contention where to challenge the politics of memory in Chile and in it, a concept of heritage that still remains monolithic and uncontroversial side.   Key words:  Heritage – Chilean Literature - Cultural Studie

A two-level enriched finite element method for a mixed problem

The simplest pair of spaces is made inf-sup stable for the mixed form of the Darcy equation. The key ingredient is to enhance the finite element spaces inside a Petrov-Galerkin framework with functions satisfying element-wise local Darcy problems with right hand sides depending on the residuals over elements and edges. The enriched method is symmetric, locally mass conservative and keeps the degrees of freedom of the original interpolation spaces. First, we assume local enrichments exactly computed and we prove uniqueness and optimal error estimates in natural norms. Then, a low cost two-level finite element method is proposed to effectively obtain enhancing basis functions. The approach lays on a two-scale numerical analysis and shows that well-posedness and optimality is kept, despite the second level numerical approximation. Several numerical experiments validate the theoretical results and compares (favourably in some cases) our results with the classical Raviart-Thomas elemen