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A DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR TIME DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS WITH HIGHER ORDER DERIVATIVES

by Yingda Cheng, Chi-wang Shu

"... Abstract. In this paper, we develop a new discontinuous Galerkin (DG) finite element method for solving time dependent partial differential equations (PDEs) with higher order spatial derivatives. Unlike the traditional local discontinuous Galerkin (LDG) method, the method in this paper can be applie ..."

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Abstract. In this paper, we develop a new discontinuous Galerkin (DG) finite element method for solving time dependent partial differential equations (PDEs) with higher order spatial derivatives. Unlike the traditional local discontinuous Galerkin (LDG) method, the method in this paper can

Local Discontinuous Galerkin Methods for High-Order Time-Dependent Partial Differential Equations

by Yan Xu, Chi-wang Shu , 2010

"... Discontinuous Galerkin (DG) methods are a class of finite element methods using discontinuous basis functions, which are usually chosen as piecewise polynomials. Since the basis functions can be discontinuous, these methods have the flexibility which is not shared by typical finite element methods, ..."

Abstract - Cited by 12 (1 self) - Add to MetaCart

) methods for solving high-order time-dependent partial differential equations (PDEs). The important ingredient of the design of LDG schemes, namely the adequate choice of numerical fluxes, is highlighted. Some of the applica-tions of the LDG methods for high-order time-dependent PDEs are also be discussed.

Redistribution of Nodes with Two Constraints in Meshless Method of Line to Time-Dependent Partial Differential Equations

by Jafar Biazar , Mohammad Hosami , Patricia J Y Wong

"... Meshless method of line is a powerful device to solve time-dependent partial differential equations. In integrating step, choosing a suitable set of points, such as adaptive nodes in spatial domain, can be useful, although in some cases this can cause ill-conditioning. In this paper, to produce smo ..."

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Meshless method of line is a powerful device to solve time-dependent partial differential equations. In integrating step, choosing a suitable set of points, such as adaptive nodes in spatial domain, can be useful, although in some cases this can cause ill-conditioning. In this paper, to produce

A Volumetric Integral Radial Basis Function Method for Time-Dependent Partial Differential Equations: I. Formulation

by E. J. Kansa, H. Power, G. E. Fasshauer, L. Ling

"... A. Local rotational and Galilean translational transformations can be obtainedto reduce the conservation equations into steady state forms for the inviscid Euler equations or Navier-Stokes equations. B. The entire set of PDEs are transformed into the method of lines approachyielding a set of coupled ..."

Abstract - Cited by 14 (1 self) - Add to MetaCart

of coupled ordinary differential equations whose homogeneous solution is exact in time. C. The spatial components are approximated by expansions of meshless RBFs;each individual RBF is volumetrically integrated at one of the sampling knots xi, yielding a collocation formulation of the method of lines

A Local Refinement Finite Element Method for Time- Dependent Partial Differential Equations," in: Trans

by Unclassified J E Flaherty, Et Al, Aug Rrlcb-tr, R- -r, Joseph E. Flaherty, Peter K. Moore - Second Army Conf. onAppl. Math, and Comput., ARO Report 85-1, U.S. Army Research Office, Research Triangle Park, NC , 1985

"... * DISCLAIME The findings in this report are not to be construed as an official Department of the Army position unless so designated by other authorized documents.- The use of trade unm(s) and/or manufacture(s) does not constitute an official indorsement or approval. DISPOSITION Destroy this report w ..."

Abstract - Cited by 5 (4 self) - Add to MetaCart

* DISCLAIME The findings in this report are not to be construed as an official Department of the Army position unless so designated by other authorized documents.- The use of trade unm(s) and/or manufacture(s) does not constitute an official indorsement or approval. DISPOSITION Destroy this report when it is no longer needed. Do not return it

MOVCOL4: A Moving Mesh Code for Fourth-Order Time-Dependent Partial Differential Equations

by R. D. Russell, Jf Williams, X. Xu , 2005

"... In this paper we develop and analyze a moving mesh code for the simulation of fourth-order PDEs based on collocation. The scheme is shown to enforce discrete conservation for problems written in a generalized conservation form. To demonstrate the breadth of applicability we present examples from bot ..."

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both Cahn-Hilliard and thin-film type equations exhibiting metastable behaviour, finite-time solution blow-up, finitetime extinction and moving interfaces. 1

VARIABLE STEP-SIZE IMPLICIT-EXPLICIT LINEAR MULTISTEP METHODS FOR TIME-DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS

by Dong Wang, Steven, J. Ruuth

"... Abstract. Implicit-explicit (IMEX) linear multistep methods are popular techniques for solving partial differential equations (PDEs) with terms of different types. While fixed time-step versions of such schemes have been developed and studied, implicit-explicit schemes also naturally arise in genera ..."

Abstract - Cited by 1 (0 self) - Add to MetaCart

Abstract. Implicit-explicit (IMEX) linear multistep methods are popular techniques for solving partial differential equations (PDEs) with terms of different types. While fixed time-step versions of such schemes have been developed and studied, implicit-explicit schemes also naturally arise