Error estimates for the hybrid finite element/finite volume methods for linear hyperbolic and convection-dominated problems

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).