By Ben Q. Li
During the last numerous years, major advances were made in constructing the discontinuous Galerkin finite aspect process for purposes in fluid movement and warmth move. definite precise positive factors of the strategy have made it appealing as a substitute for different renowned tools similar to finite quantity and finite parts in thermal fluids engineering analyses. This booklet is written as an introductory textbook at the discontinuous finite aspect technique for senior undergraduate and graduate scholars within the sector of thermal technological know-how and fluid dynamics. It may also be used as a reference e-book for researchers and engineers who intend to take advantage of the tactic for examine in computational fluid dynamics and warmth move. a significant portion of this booklet has been utilized in a direction for computational fluid dynamics and warmth move for senior undergraduate and primary yr graduate scholars. It additionally has been utilized by a few graduate scholars for self-study of the fundamentals of discontinuous finite parts. This monograph assumes that readers have a uncomplicated figuring out of thermodynamics, fluid mechanics and warmth move and a few historical past in numerical research. wisdom of constant finite parts isn't really helpful yet should be useful. The e-book covers the applying of the strategy for the simulation of either macroscopic and micro/nanoscale fluid movement and warmth move phenomena.
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Additional resources for Discontinuous Finite Elements in Fluid Dynamics and Heat Transfer
This is another important feature that makes this method useful for fluid flow calculations. Computational fluid dyanmics is an evolving subject, and very recent developments in the area are discussed in . In the literature, the discontinuous finite element method is also called the discontinuous Galerkin method, or the discontinuous Galerkin finite element method, or the discontinuous method [1, 2, 3, 5, 6]. These terms will be used interchangeably throughout this book. This chapter introduces the basic ideas of the discontinuous finite element method through simple and illustrative examples.
London: Cambridge University Press, 1930. 2 Discontinuous Finite Element Procedures The discontinuous finite element method makes use of the same function space as the continuous method, but with relaxed continuity at interelement boundaries. It was first introduced by Reed and Hill  for the solution of the neutron transport equation, and its history and recent development have been reviewed by Cockburn et al. [2, 3]. The essential idea of the method is derived from the fact that the shape functions can be chosen so that either the field variable, or its derivatives or generally both, are considered discontinuous across the element boundaries, while the computational domain continuity is maintained.
New York: Springer-Verlag, Feb. 2000; 135–146.  Biswas R, Devine KD, Flaherty JE. Parallel Adaptive Finite Element Methods for Conservation Laws. Appl. Numer. Math. 1994; 14(1): 255–283. 3 Shape Functions and Elemental Calculations Like its continuous counterpart, the discontinuous finite element method employs shape functions for local approximations. The use of 1-D linear shape functions was demonstrated in the last chapter for the discontinuous Galerkin solution of boundary and initial value problems.
Discontinuous Finite Elements in Fluid Dynamics and Heat Transfer by Ben Q. Li