A discontinuous hp finite element method for diffusion problems: 1-D analysis
作者： I. Babuška , C.E. Baumann , J.T. Oden
DOI: 10.1016/S0898-1221(99)00117-0
关键词: Boundary knot method 、 Discontinuous Deformation Analysis 、 Mathematics 、 Extended finite element method 、 Boundary value problem 、 Stability (learning theory) 、 Discontinuous Galerkin method 、 Finite element method 、 Mathematical analysis 、 Mixed finite element method
摘要: Abstract This paper presents the mathematical analysis of a new variant discontinuous Galerkin method which is applicable to numerical solution diffusion problems, not requiring auxiliary variables such as those used in mixed methods. The focus this study on class linear second-order boundary value problems for we prove stability and priori error estimates both finite- infinite-dimensional spaces.
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sci-hub.se 参考文章(16)
Bernardo Cockburn, Chi-Wang Shu, Claes Johnson, Eitan Tadmor, Bernardo Cockburn, An introduction to the Discontinuous Galerkin method for convection-dominated problems Lecture Notes in Mathematics. pp. 150- 268 ,(1998) , 10.1007/BFB0096353
Abdul Kadir Aziz, The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations Academic Press. ,(1972)
J.A Hendry, L.M Delves, The global element method applied to a harmonic mixed boundary value problem Journal of Computational Physics. ,vol. 33, pp. 33- 44 ,(1979) , 10.1016/0021-9991(79)90026-3
J.Tinsley Oden, Ivo Babuŝka, Carlos Erik Baumann, A DiscontinuoushpFinite Element Method for Diffusion Problems Journal of Computational Physics. ,vol. 146, pp. 491- 519 ,(1998) , 10.1006/JCPH.1998.6032
Peter Percell, Mary Fanett Wheeler, A Local Residual Finite Element Procedure for Elliptic Equations SIAM Journal on Numerical Analysis. ,vol. 15, pp. 705- 714 ,(1978) , 10.1137/0715047
L. M. DELVES, C. A. HALL, An Implicit Matching Principle for Global Element Calculations Ima Journal of Applied Mathematics. ,vol. 23, pp. 223- 234 ,(1979) , 10.1093/IMAMAT/23.2.223
Igor Lomtev, George Em Karniadakis, A discontinuous Galerkin method for the Navier–Stokes equations International Journal for Numerical Methods in Fluids. ,vol. 29, pp. 587- 603 ,(1999) , 10.1002/(SICI)1097-0363(19990315)29:5<587::AID-FLD805>3.0.CO;2-K
Bernardo Cockburn, Chi-Wang Shu, The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems SIAM Journal on Numerical Analysis. ,vol. 35, pp. 2440- 2463 ,(1998) , 10.1137/S0036142997316712
I. Lomtev, C.B. Quillen, G.E. Karniadakis, Spectral/hp Methods for Viscous Compressible Flows on Unstructured 2D Meshes Journal of Computational Physics. ,vol. 144, pp. 325- 357 ,(1998) , 10.1006/JCPH.1997.5831
Douglas N. Arnold, An Interior Penalty Finite Element Method with Discontinuous Elements SIAM Journal on Numerical Analysis. ,vol. 19, pp. 742- 760 ,(1982) , 10.1137/0719052