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Cubic superconvergent finite volume element method for one-dimensional elliptic and parabolic equations

Guanghua Gao, Tongke Wang
2010 Journal of Computational and Applied Mathematics  
In this paper, a cubic superconvergent finite volume element method based on optimal stress points is presented for one-dimensional elliptic and parabolic equations.  ...  For elliptic problem, it is proved that the method has optimal third order accuracy with respect to H 1 norm and fourth order accuracy with respect to L 2 norm.  ...  Cubic superconvergent finite volume element method for one-dimensional elliptic equation Consider the following one-dimensional elliptic equation with boundary values of mixed type on I = [a, b] − d dx  ... 
doi:10.1016/ fatcat:pae5tnhvwbdupggg7xqg2d76my

Page 3049 of Mathematical Reviews Vol. , Issue 96e [page]

1996 Mathematical Reviews  
The author uses generalized difference methods to discuss elliptic second-order differential equations in one- and two-dimensional domains.  ...  Error estimates of optimal order are derived for both the new mixed finite element and an associated finite volume method.  ... 

Page 7048 of Mathematical Reviews Vol. , Issue 99j [page]

1999 Mathematical Reviews  
(F-PARIS11-AD; Orsay) The finite volume method for an elliptic-parabolic equation. (English summary) Proceedings of the Algoritmy’97 Conference on Scientific Computing (Zuberec). Acta Math. Univ.  ...  a frequency-domain finite element method for parabolic problems with a Neumann boundary condition.  ... 

Page 697 of Mathematical Reviews Vol. , Issue 81B [page]

1981 Mathematical Reviews  
E. 81b:65 104 Solution by the relaxation iteration method of finite element method schemes for elliptic equations of order 2n. (Russian) Cisl. Metody Meh. Splosn. Sredy 8 (1977), no. 7, 72-86.  ...  This paper continues the authors’ studies on the application of curvilinear finite elements to schemes for solving Dirichlet boundary value problems for linear elliptic equations of order 2n of the form  ... 

Superconvergent biquadratic finite volume element method for two-dimensional Poisson's equations

Tongke Wang, Yuesheng Gu
2010 Journal of Computational and Applied Mathematics  
kind of biquadratic finite volume element method is presented for two-dimensional Poisson's equations by restricting the optimal stress points of biquadratic interpolation as the vertices of control volumes  ...  MSC: 65N12 65N15 Keywords: Poisson's equation Biquadratic finite volume element method Alternating direction method Optimal stress point Error estimate Superconvergence a b s t r a c t In this paper, a  ...  Plexousakis and Zouraris [16] derived a class of high order finite volume methods for solving one dimensional elliptic equations. Yang et al.  ... 
doi:10.1016/ fatcat:eoipnca37jecbfmaq2y6l2xnh4

subject index 10 volumes

2005 Journal of Computational and Applied Mathematics  
m-Function 171 93, 411 Mittag-Leffler functions 171 39 Mixed boundary value problem 174 251 Mixed finite elements 174 213 Mixed finite volume element method 172 117 Mixing layer problems 173 57  ...  er kernel 179 327 Finite abelian groups 174 165 Finite difference approximation 172 65 Finite difference method 177 287 Finite difference schemes 176 59 Finite differences 180 173 Finite element  ... 
doi:10.1016/s0377-0427(05)00274-8 fatcat:lnl66qx5lngarjw7i3ducv7qta

Discontinuous control-volume/finite-element method for advection–diffusion problems

G. Stipcich, M. Piller, M. Pivetta, L. Zovatto
2011 Computers & Fluids  
The discontinuous control-volume/finite-element method is applied to the one-dimensional advection-diffusion equation.  ...  A mixed formulation is followed, where the constitutive equation for the diffusive flux is not substituted into the conservation equation for the transported scalar.  ...  remarks The discontinuous control-volume finite-element method is applied to the one-dimensional advection-diffusion equation and to the two-dimensional diffusion equation.  ... 
doi:10.1016/j.compfluid.2011.08.014 fatcat:tuav2hlddndunfm2y6ziavr664

Global superconvergence of Adini's elements coupled with the Trefftz method for singular problems

Hung-Tsai Huang, Zi-Cai Li
2003 Engineering analysis with boundary elements  
This paper reports new results of the Trefftz method (i.e. the boundary approximation method (BAM) by Li [Combined Methods for Elliptic Equations with Singularities, Interfaces and Infinities, 1998] using  ...  First, the computational aspects and numerical experiments are provided for the global superconvergence of Adini's elements for the Poisson equation.  ...  Acknowledgements We are greatly grateful to Professors Alexander Cheng and Ningning Yan as well as reviewers for their valuable comments and suggestions in this paper.  ... 
doi:10.1016/s0955-7997(02)00136-4 fatcat:c4ga5677sbdtbft5ww6dsy73mm

Newsletter on computational and applied mathematics

1986 Journal of Computational and Applied Mathematics  
Mathematical Theory of Finite Elements Engineering and Scientific Applications of Finite Elements Computational Techniques for the Implementation of Finite Element Methods Boundary Element Methods and  ...  . : Superconvergence of a collocation-type method for Hammerstein equations (April 1986).  ...  AVAILABLESXTWARE A MODULAR FINITE ELEMENT PROGRAM PACKAGE The annual fee is small, just to cover the tape, the mailings and report-distribution costs. The package is available on a magnetic tape.  ... 
doi:10.1016/0377-0427(86)90011-7 fatcat:hphocaxdr5bthbvzj6zee7nu7m

Author Index Volume 235 (2011)

2011 Journal of Computational and Applied Mathematics  
Chen, A reduced finite volume element formulation and numerical simulations based on POD for parabolic problems 2098-2111 Luxemburg, L.A. and P.R.  ...  Rivière, On the coupling of finite volume and discontinuous Galerkin method for elliptic problems 2193-2204 a derivative nonlinear Schrödinger equation: Elliptic integrals of the third kind 3825-  ... 
doi:10.1016/s0377-0427(11)00383-9 fatcat:iydszqpkezgivirtbnwhpwere4

A Hybrid Method and Unified Analysis of Generalized Finite Differences and Lagrange Finite Elements [article]

Rebecca Conley, Xiangmin Jiao, Tristan J. Delaney
2020 arXiv   pre-print
Finite differences, finite elements, and their generalizations are widely used for solving partial differential equations, and their high-order variants have respective advantages and disadvantages.  ...  for some special cases on regular grids.  ...  Acknowledgments This work was supported in part by DoD-ARO under contract #W911NF0910306 and also in part under the Scientific Discovery through Advanced Computing  ... 
arXiv:1603.09325v7 fatcat:j7zksdemtff2fdpf4hxofuil7a

The mathematics of finite elements and applications

1989 International Journal of Engineering Science  
That theory has been shown to produce good -"--" results for general elliptic systems and general hp-finite element methods.  ...  C JOHNSON Adaptive finite element methods in compti ational mechanics We give an overview of our recent work on adaptive finite element methods for problems in solid and fluid mechanics including elasticity  ...  of hyperbolic, parabolic, and elliptic equations.  ... 
doi:10.1016/0020-7225(89)90012-8 fatcat:z6hknn325re4tbssbqqzmcketa


1986 Mathematics of Computation  
Tinsley & Carey, Graham F. 37 Computational Techniques for Differential Equations Finite Elements, Mathematical Aspects 65N30 Finite Elements, Rayleigh-Ritz and Galerkin Methods, Finite Methods  ...  A. 46 371 O'Riordan, Eugene 8l A Uniformly Accurate Finite-Element Method for Stynes, Martin a Singularly Perturbed One-Dimensional Reaction-Diffusion Problem. 47 555 O'Riordan, Eugene 8l  ... 
doi:10.1090/s0025-5718-86-99762-0 fatcat:pv37gstohzburgo6grl5qbyxx4

A positivity-preserving finite element method for chemotaxis problems in 3D

Robert Strehl, Andriy Sokolov, Dmitri Kuzmin, Dirk Horstmann, Stefan Turek
2013 Journal of Computational and Applied Mathematics  
We present an implicit finite element method for a class of chemotaxis models in three spatial dimensions.  ...  To give a flavor of more complex and realistic chemotactic applications, we investigate the pattern dynamics and aggregating behavior of the bacteria Escherichia coli and Salmonella typhimurium.  ...  For example, Nadin, Perthame and Ryzhik [50] proved the existence of traveling wave solutions to a one-dimensional parabolic-elliptic version of (8) if the growth term is either a Fisher/KPP type or  ... 
doi:10.1016/ fatcat:gkohvrcah5hx5ffmlmjtpoxlza

Parallel Partitioning Strategies for the Adaptive Solution of Conservation Laws [chapter]

Karen D. Devine, Joseph E. Flaherty, Raymond M. Loy, Stephen R. Wheat
1995 IMA Volumes in Mathematics and its Applications  
Directorate for information Ooerations and Reoorts. '2 IS Jefferson Däv'iH--wav Suite 12C4 Arlington VÄ 22202-4302. and to fe 0";:e o* Management and Budget. oaoerwcrK Reduction Project (S7C4019S), Washington  ...  Sena comments regaraing this buraen estimate or anv otner aspect of tms collection of information "mcluaing sugaestions for reducing this Duraen iz Washington Headquarters Services.  ...  A basis for the local space Sj may be denned using products of one-dimensional Legendre polynomials, as distinct from hierarchical bases for elliptic and parabolic systems [34] which use integrals of  ... 
doi:10.1007/978-1-4612-4248-2_12 fatcat:rer2hhnt7fdsraywi63vwvltmm
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