An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation
Mathematics of Computation
A class of implicit upwind schemes for Euler simulations with unstructured meshes
Journal of Computational Physics
Journal of Computational Physics
Combined finite element-finite volume solution of compressible flow
Modelling 94 Proceedings of the 1994 international symposium on Mathematical modelling and computational methods
SIAM Journal on Numerical Analysis
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Journal of Computational and Applied Mathematics
Error estimates for a finite element-finite volume discretization of convection-diffusion equations
Applied Numerical Mathematics
Hi-index | 7.29 |
In this paper, we establish the error estimates for the generalized hybrid finite element/finite volume methods we have introduced in our earlier work (J. Comput. Appl. Math. 139 (2002) 323; Comm. Appl. Anal. 5(1) (2001) 91). These estimates are obtained for linear hyperbolic and convection-dominated convection-diffusion problems. Our analysis is performed for general mesh of a bounded polygonal domain of Rn satisfying the minimum angle condition. Our errors estimates are new and represent significant improvements over the previously known error estimates established for the streamline diffusion and discontinuous Galerkin methods applied to hyperbolic and convection dominated problems (Math. Comp. 46 (1986) 1; Comput. Methods Appl. Mech. Eng. 45 (1984) 285; in: C. de Boor (Ed.), Mathematical Aspects of Finite Elements in Partial Differential Equations, Academic Press, New York, 1974).