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
Computer Methods in Applied Mechanics and Engineering
Journal of Computational Physics
A parallel hp-adaptive discontinuous Galerkin method for hyperbolic conservation laws
Applied Numerical Mathematics - Special issue on adaptive mesh refinement methods for CFD applications
A discontinuous hp finite element method for diffusion problems
Journal of Computational Physics
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
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In this paper we introduce a generalized hybrid finite element/finite volume methods. We then establish the mathematical foundations of the hybrid finite element/finite volume methods for linear hyperbolic, convection-dominated convection-diffusion, and convection-diffusion problems. More precisely, we study the stability and convergence properties of this hybrid scheme for such problems. This analysis is performed for general mesh of a bounded polygonal domain of Rn (n = 2 or 3) satisfying the minimum angle condition. Our stability results are completely new and solve important open problems related to whether or not there exist approximations of hyperbolic and convection dominated problems having such stability properties.