Error estimation of a quadratic finite volume method on right quadrangular prism grids
Journal of Computational and Applied Mathematics
Unified Analysis of Finite Volume Methods for the Stokes Equations
SIAM Journal on Numerical Analysis
Convergence of the discontinuous finite volume method for elliptic problems with minimal regularity
Journal of Computational and Applied Mathematics
Higher-order finite volume methods for elliptic boundary value problems
Advances in Computational Mathematics
Superconvergence for discontinuous Galerkin finite element methods by L2-projection methods
Computers & Mathematics with Applications
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We establish a general framework for analyzing the class of finite volume methods which employ continuous or totally discontinuous trial functions and piecewise constant test functions. Under the framework, optimal order convergence in the $H^1$ and $L^2$ norms can be obtained in a natural and systematic way for classical finite volume methods and new finite volume methods such as discontinuous finite volume methods applied to second order elliptic problems.