2,116 research outputs found
Hybrid Discontinuous Galerkin methods with relaxed
No full textThe present work is the second part of a pair of papers, considering Hybrid Discontinuous Galerkin methods with relaxed H(div)-conformity. The first part mainly dealt with presenting a robust analysis with respect to the mesh size h and the introduction of a reconstruction operator to restore divergence-conformity and pressure robustness (pressure independent velocity error estimates) using a modified force discretization. The aim of this part is the presentation of a high order polynomial robust analysis for the relaxed H(div)-conforming Hybrid Discontinuous Galerkin discretization of the two dimensional Stokes problem. It is based on the recently proven polynomial robust LBB-condition for BDM elements, Lederer and Schöberl (IMA J. Numer. Anal. (2017)) and is derived by a direct approach instead of using a best approximation Céa like result. We further treat the impact of the reconstruction operator on the hp analysis and present a numerical investigation considering polynomial robustness. We conclude the paper presenting an efficient operator splitting time integration scheme for the Navier–Stokes equations which is based on the methods recently presented in Lehrenfeld and Schöberl (Comp. Methods Appl. Mech. Eng. 307 (2016) 339–361) and includes the ideas of the reconstruction operator
Trefftz discontinuous Galerkin discretization for the Stokes problem
No full textAbstract
We introduce a new discretization based on a polynomial Trefftz-DG method for solving the Stokes equations. Discrete solutions of this method fulfill the Stokes equations pointwise within each element and yield element-wise divergence-free solutions. Compared to standard DG methods, a strong reduction of the degrees of freedom is achieved, especially for higher polynomial degrees. In addition, in contrast to many other Trefftz-DG methods, our approach allows us to easily incorporate inhomogeneous right-hand sides (driving forces) by using the concept of the embedded Trefftz-DG method. On top of a detailed a priori error analysis, we further compare our approach to other (hybrid) discontinuous Galerkin Stokes discretizations and present numerical examples
Divergence‐free tangential finite element methods for incompressible flows on surfaces
No full textIn this work we consider the numerical solution of incompressible flows on two-dimensional manifolds. Whereas the compatibility demands of the velocity and the pressure spaces are known from the flat case one further has to deal with the approximation of a velocity field that lies only in the tangential space of the given geometry. Abandoning -conformity allows us to construct finite elements which are -- due to an application of the Piola transformation -- exactly tangential. To reintroduce continuity (in a weak sense) we make use of (hybrid) discontinuous Galerkin techniques. To further improve this approach, -conforming finite elements can be used to obtain exactly divergence-free velocity solutions. We present several new finite element discretizations. On a number of numerical examples we examine and compare their qualitative properties and accuracy.Austrian Science Fund http://dx.doi.org/10.13039/50110000242
Trefftz Discontinuous Galerkin discretization for the Stokes problem
No full textWe introduce a new discretization based on the Trefftz-DG method for solving
the Stokes equations. Discrete solutions of a corresponding method fulfill the
Stokes equation pointwise within each element and yield element-wise
divergence-free solutions. Compared to standard DG methods, a strong reduction
of the degrees of freedom is achieved, especially for higher order polynomial
degrees. In addition, in contrast to many other Trefftz-DG methods, our
approach allows to easily incorporate inhomogeneous right hand sides (driving
forces) by using the concept of the embedded Trefftz-DG method.
On top of a detailed a priori error analysis, we further compare our approach
to standard discontinuous Galerkin Stokes discretizations and present numerical
examples
Trefftz Discontinuous Galerkin discretization for the Stokes problem
No full textWe introduce a new discretization based on the Trefftz-DG method for solving
the Stokes equations. Discrete solutions of a corresponding method fulfill the
Stokes equation pointwise within each element and yield element-wise
divergence-free solutions. Compared to standard DG methods, a strong reduction
of the degrees of freedom is achieved, especially for higher order polynomial
degrees. In addition, in contrast to many other Trefftz-DG methods, our
approach allows to easily incorporate inhomogeneous right hand sides (driving
forces) by using the concept of the embedded Trefftz-DG method.
On top of a detailed a priori error analysis, we further compare our approach
to standard discontinuous Galerkin Stokes discretizations and present numerical
examples
Hybrid Discontinuous Galerkin Methods with Relaxed H(div)-Conformity for Incompressible Flows. Part I
No full textWe propose a new discretization method for the Stokes equations. The method is an improved version of the method recently presented in [C. Lehrenfeld and J. Schöberl, Comp. Meth. Appl. Mech. Eng., 361 (2016)] which is based on an ({div})ehBconforming finite element space and a hybrid discontinuous Galerkin (HDG) formulation of the viscous forces. ({div})ehBconformity results in favorable properties such as pointwise divergence-free solutions and pressure robustness. However, for the approximation of the velocity with a polynomial degree on every facet of the mesh. In view of the superconvergence property of other HDG methods, where only unknowns of polynomial degree -1 (possibly after a local postprocessing), this is suboptimal. The key idea in this paper is to slightly relax the ({div})ehBconformity so that only unknowns of polynomial degree -1$ are involved for normal continuity. This allows for optimality of the method also in the sense of superconvergent HDG methods. In order not to lose the benefits of ({div})ehBconformity, we introduce a cheap reconstruction operator which restores pressure robustness and pointwise divergence-free solutions and suits well to the finite element space with relaxed ({div})ehBconformity. We present this new method, carry out a thorough ehBversion error analysis, and demonstrate the performance of the method on numerical examples. Read More: https://epubs.siam.org/doi/10.1137/17M113807
On reference solutions and the sensitivity of the 2D Kelvin-Helmholtz instability problem
No full textTwo-dimensional Kelvin-Helmholtz instability problems are popular examples for assessing discretizations for incompressible flows at high Reynolds number. Unfortunately, the results in the literature differ considerably. This paper presents computational studies of a Kelvin-Helmholtz instability problem with high order divergence-free finite element methods. Reference results in several quantities of interest are obtained for three different Reynolds numbers up to the beginning of the final vortex pairing. A mesh-independent prediction of the final pairing is not achieved due to the sensitivity of the considered problem with respect to small perturbations. A theoretical explanation of this sensitivity to small perturbations is provided based on the theory of self-organization of 2D turbulence. Possible sources of perturbations that arise in almost any numerical simulation are discussed
Motion and mobility in the realist novels of Philip K Dick
No full textThis essay explores the ways that ideas of motion and mobility support readings of Philip K Dick's early novels that take full account of the changing geographical context. They are set during a period of rapid suburban expansion, the building of the interstate and the spread of automobility through car ownership, and their characters frequently exist in a state between continuity through conformity and the potential for change. The open ended forms of the novels reflect a world around Dick that was still under construction, and where alternative realities can be glimpsed between incomplete materialities
ENTREVISTA COM PHILIP SMITH, DIRETOR DO L. M. MONTGOMERY INSTITUTE
No full textThis text aims to present an interview with Dr. Philip Smith, professor of Psychology at the University of Prince Edward Island (UPEI) and chair of the L. M. Montgomery Institute (LMMI). The L. M. Montgomery Institute, located in Charlottetown, Canada, provides a dynamic research center focused on the life and work of the Canadian author L. M. Montgomery (Lucy Maud Montgomery). Montgomery is best known for her book Anne of Green Gables, published in 1908 by the L. C. Page Company. She also wrote twenty novels, an autobiography, and hundreds of short stories and poems. The LMMI, founded in 1993 by Dr. Elizabeth Epperly, has been dedicated to promoting research into the life, work, and culture of L. M. Montgomery. This interview results from a training program conducted at the University of Prince Edward Island, with funding provided by the CAPES Foundation (Process n.: 88887.838993/2023-00).
Keywords: L. M. Montgomery. L. M. Montgomery Institute. Philip Smith.Este texto tem por objetivo apresentar uma entrevista com Dr. Philip Smith, professor de Psicologia da Universidade da Ilha do Príncipe Eduardo (UPEI) e diretor do L. M. Montgomery Institute (LMMI), instituto localizado em Charlottetown, no Canadá, que se propõe a apoiar pesquisas relacionadas à vida e obra da autora canadense L. M. Montgomery (Lucy Maud Montgomery). Montgomery é reconhecida principalmente pela obra Anne of Green Gables, publicada em 1908, pela editora L. C. Page. Contudo, no decorrer de sua vida, escreveu vinte romances, uma autobiografia, bem como centenas de contos e poemas. O Instituto, fundado em 1993 pela professora Dra. Elizabeth Epperly, tem se dedicado à divulgação, pesquisa e elaboração de congressos bienais a respeito da vida, produção literária e cultural de L. M. Montgomery. Esta entrevista é fruto de uma capacitação realizada na Universidade da Ilha do Príncipe Eduardo, no âmbito do Programa CAPES-PRINT, financiada pela CAPES (Processo nº: 88887.838993/2023-00).
Palavras-chave: L. M. Montgomery; L. M. Montgomery Institute; Philip Smith
Financial safety nets and incentive structures in Latin America
No full textThe literature on safety nets has become technically more precise by drawing on advances in contract theory and optimal governance structure. This paper begins with a treatment of some aspects of the theory. The author's approach draws more on institutional economics, and more precisely on the approach taken by Kindleberger (1978), in the sense that he believes the design of good financial safety nets for Latin America depends upon an understanding of the way that formal ex-ante safety nets have broken down during times of crisis over the past one hundred years. In this paper then author explores issues surrounding safety nets for financial systems in small open economies like those in Latin America. The starting point in Section 2 is the idea that asymmetric information will generally restrict the scope for lending to potential borrowers. Section 3 shows that government regulation of financial intermediaries can frequently lower the cost of lending. Section 4 discusses the creation of central banks in Latin America in the 1920s as an innovation to promote financial deepening. Section 5 shows that the extension of the safety net to depositors is a relatively new and untested development. Section 6 concludes with a discussion of the design of safety nets that takes into account the principles developed in the paper.Financial Crisis Management&Restructuring,Payment Systems&Infrastructure,Financial Intermediation,Banks&Banking Reform,Labor Policies,Financial Intermediation,Financial Crisis Management&Restructuring,Economic Theory&Research,Environmental Economics&Policies,Banks&Banking Reform
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