Journal•ISSN: 0008-0624
Calcolo
Springer Science+Business Media
About: Calcolo is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Numerical analysis & Finite element method. It has an ISSN identifier of 0008-0624. Over the lifetime, 1428 publications have been published receiving 15107 citations.
Topics: Numerical analysis, Finite element method, Theory of computation, Discretization, Matrix (mathematics)
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TL;DR: In this paper, a new velocity-pressure finite element for the computation of Stokes flow is presented, which satisfies the usual inf-sup condition and converges with first order for both velocities and pressure.
Abstract: We present in this paper a new velocity-pressure finite element for the computation of Stokes flow. We discretize the velocity field with continuous piecewise linear functions enriched by bubble functions, and the pressure by piecewise linear functions. We show that this element satisfies the usual inf-sup condition and converges with first order for both velocities and pressure. Finally we relate this element to families of higer order elements and to the popular Taylor-Hood element.
1,084 citations
TL;DR: A variant of the classical weighted least-squares stabilization for the Stokes equations has improved accuracy properties, especially near boundaries, and is based on local projections of the residual terms which are used in order to achieve consistency of the method.
Abstract: We present a variant of the classical weighted least-squares stabilization for the Stokes equations. Compared to the original formulation, the new method has improved accuracy properties, especially near boundaries. Furthermore, no modification of the right-hand side is needed, and implementation is simplified, especially for generalizations to more complicated equations. The approach is based on local projections of the residual terms which are used in order to achieve consistency of the method, avoiding local evaluation of the strong form of the differential operator. We prove stability and give a priori and a posteriori error estimates. We show convergence of an iterative method which uses a simplified stabilized discretization as preconditioner. Numerical experiments indicate that the approach presented is at least as accurate as the original method, but offers some algorithmic advantages. The ideas presented here also apply to the Navier–Stokes equations. This is the topic of forthcoming work.
380 citations
TL;DR: In this article, the first integral method was used to construct exact solutions of the Wu-Zhang system, which is based on the ring theory of commutative algebra, and the results obtained confirm that the proposed method is an efficient technique for analytic treatment of a wide variety of nonlinear conformable time-fractional partial differential equations.
Abstract: In this paper, the first integral method is used to construct exact solutions of the time-fractional Wu---Zhang system. Fractional derivatives are described by conformable fractional derivative. This method is based on the ring theory of commutative algebra. The results obtained confirm that the proposed method is an efficient technique for analytic treatment of a wide variety of nonlinear conformable time-fractional partial differential equations.
344 citations
TL;DR: A numerical scheme to compute Saint-Venant equations with a source term, due to the bottom topography, in a one-dimensional framework which satisfies the following theoretical properties: it preserves the steady state of still water, satisfies an entropy inequality, preserves the non-negativity of the height of water and remains stable with a discontinuous bottom.
Abstract: The aim of this paper is to present a numerical scheme to compute Saint-Venant equations with a source term, due to the bottom topography, in a one-dimensional framework, which satisfies the following theoretical properties: it preserves the steady state of still water, satisfies an entropy inequality, preserves the non-negativity of the height of water and remains stable with a discontinuous bottom This is achieved by means of a kinetic approach to the system, which is the departing point of the method developed here In this context, we use a natural description of the microscopic behavior of the system to define numerical fluxes at the interfaces of an unstructured mesh We also use the concept of cell-centered conservative quantities (as usual in the finite volume method) and upwind interfacial sources as advocated by several authors We show, analytically and also by means of numerical results, that the above properties are satisfied
303 citations
TL;DR: In this paper, the problem of finding maximal common subgraphs of two given graphs is considered and a technique is described by which this problem can be stated as a problem of deriving maximal compatibility classes.
Abstract: In this note the problem is considered of finding maximal common subgraphs of two given graphs. A technique is described by which this problem can be stated as a problem of deriving maximal compatibility classes. A known «maximal compatibility classes» algorithm can then be used to derive maximal common subgraphs. The same technique is shown to apply to the classical subgraph isomorphism problem.
244 citations