A New Discontinuous Finite Volume Method for Elliptic Problems

We develop and analyze a new discontinuous finite volume method for second order elliptic problems with tensor coefficients. An optimal order error estimate is obtained in a mesh dependent norm. An L2 -error estimate is also obtained.

[1]  B. Rivière,et al.  Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. Part I , 1999 .

[2]  W. H. Reed,et al.  Triangular mesh methods for the neutron transport equation , 1973 .

[3]  J. Douglas,et al.  Interior Penalty Procedures for Elliptic and Parabolic Galerkin Methods , 1976 .

[4]  J. Aubin,et al.  Approximation des problèmes aux limites non homogènes pour des opérateurs non linéaires , 1970 .

[5]  J. Nitsche Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind , 1971 .

[6]  I. Babuska,et al.  Nonconforming Elements in the Finite Element Method with Penalty , 1973 .

[7]  S. Rebay,et al.  A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier-Stokes Equations , 1997 .

[8]  I. Babuska,et al.  A DiscontinuoushpFinite Element Method for Diffusion Problems , 1998 .

[9]  Bernardo Cockburn,et al.  Quantum hydrodynamic simulation of hysteresis in the resonant tunneling diode at 300 K , 1995, Journal of Computational Electronics.

[10]  Panayot S. Vassilevski,et al.  A general mixed covolume framework for constructing conservative schemes for elliptic problems , 1999, Math. Comput..

[11]  Panayot S. Vassilevski,et al.  Finite volume methods for convection-diffusion problems , 1996 .

[12]  So-Hsiang Chou,et al.  Analysis and convergence of a covolume method for the generalized Stokes problem , 1997, Math. Comput..

[13]  Douglas N. Arnold,et al.  Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems , 2001, SIAM J. Numer. Anal..

[14]  Chaoqun Liu,et al.  The finite volume-element method (FVE) for planar cavity flow , 1989 .

[15]  Do Y. Kwak,et al.  A Covolume Method Based on Rotated Bilinears for the Generalized Stokes Problem , 1998 .

[16]  I. Babuska The Finite Element Method with Penalty , 1973 .

[17]  Chi-Wang Shu,et al.  The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV. The multidimensional case , 1990 .

[18]  D. Arnold An Interior Penalty Finite Element Method with Discontinuous Elements , 1982 .