Topic
Piecewise
About: Piecewise is a research topic. Over the lifetime, 21064 publications have been published within this topic receiving 432096 citations. The topic is also known as: piecewise-defined function & hybrid function.
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TL;DR: One of the books that can be recommended for new readers is piecewise smooth dynamical systems, which is not kind of difficult book to read.
Abstract: Preparing the books to read every day is enjoyable for many people. However, there are still many people who also don't like reading. This is a problem. But, when you can support others to start reading, it will be better. One of the books that can be recommended for new readers is piecewise smooth dynamical systems. This book is not kind of difficult book to read. It can be read and understand by the new readers.
324 citations
TL;DR: In this paper, an extension of the Kirchhoffer's formula for radiation from a closed surface to surfaces moving at speeds below the wave propagation speed is presented. But it is only applied to surfaces that are piecewise smooth.
322 citations
TL;DR: In this paper, the authors derived global W1,∞ and piecewise C1,α estimates for solutions to divergence form elliptic equations with piecewise Holder continuous coefficients, and the novelty of these estimates is that, even though they depend on the shape and on the size of the surfaces of discontinuity of the coefficients, they are independent of the distance between these surfaces.
Abstract: In this paper we derive global W1,∞ and piecewise C1,α estimates for solutions to divergence form elliptic equations with piecewise Holder continuous coefficients. The novelty of these estimates is that, even though they depend on the shape and on the size of the surfaces of discontinuity of the coefficients, they are independent of the distance between these surfaces.
320 citations
TL;DR: In this article, the authors discuss the application of virtual elements to linear plate bending problems, in the Kirchhoff-love formulation, and show that the treatment of the C 1 -continuity condition is much easier than for traditional finite elements.
319 citations
01 Jan 1993
TL;DR: In this article, an upwind finite-volume scheme was proposed for solving scalar advection-diffusion equations as well as the Euler and Navier-Stokes equations.
Abstract: This paper presents recent improvements in high-order K-exact reconstruction on unstructured meshes. The new reconstruction procedures are incorporated into a basic upwind finite-volume scheme suitable for solving scalar advection-diffusion equations as well as the Euler and Navier-Stokes equations. Numerical calculations are performed comparing the present method with lower order accurate reconstruction procedures (piecewise constant and piecewise linear) and various competing technologies such as the fluctuation splitting method of Roe (1987) and Deconinck et al. (1992) and a system-variant of the streamline diffusion Petrov-Galerkin method developed by Hansbo (1991) and Hansbo and Johnson (1991). Five test problems are used in the numerical comparisons: scalar circular advection, transonic and supersonic Euler flow, laminar boundary-layer flow, and general compressible Navier-Stokes flow.
316 citations