Read Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives

Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives

Jue Yan

4.9/5 (21677 ratings)

Description:In this paper we review the existing and develop new local discontinuous Galerkin methods for solving time dependent partial differential equations with higher order derivatives in one and multiple space dimensions. We review local discontinuous Galerkin methods for convection diffusion equations involving second derivatives and for KdV type equations involving third derivatives. We then develop new local discontinuous Galerkin methods for the time dependent bi-harmonic type equations involving fourth derivatives, and partial differential equations involving fifth derivatives. For these new methods we present correct interface numerical fluxes and prove L2 stability for general nonlinear problems. Preliminary numerical examples are shown to illustrate these methods. Finally, we present new results on a post-processing technique, originally designed for methods with good negative-order error estimates, on the local discontinuous Galerkin methods applied to equations with higher derivatives. Numerical experiments show that this technique works as well for the new higher derivative cases, in effectively doubling the rate of convergence with negligible additional computational cost, for linear as well as some nonlinear problems, with a local uniform mesh.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives. To get started finding Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives, you are right to find our website which has a comprehensive collection of manuals listed.
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Pages: 24

Format: PDF, EPUB & Kindle Edition

Publisher: —

Release: 2002

ISBN: ZmRFAQAAMAAJ

Description: In this paper we review the existing and develop new local discontinuous Galerkin methods for solving time dependent partial differential equations with higher order derivatives in one and multiple space dimensions. We review local discontinuous Galerkin methods for convection diffusion equations involving second derivatives and for KdV type equations involving third derivatives. We then develop new local discontinuous Galerkin methods for the time dependent bi-harmonic type equations involving fourth derivatives, and partial differential equations involving fifth derivatives. For these new methods we present correct interface numerical fluxes and prove L2 stability for general nonlinear problems. Preliminary numerical examples are shown to illustrate these methods. Finally, we present new results on a post-processing technique, originally designed for methods with good negative-order error estimates, on the local discontinuous Galerkin methods applied to equations with higher derivatives. Numerical experiments show that this technique works as well for the new higher derivative cases, in effectively doubling the rate of convergence with negligible additional computational cost, for linear as well as some nonlinear problems, with a local uniform mesh.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives. To get started finding Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

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Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives

Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives

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