Error estimation of a quadratic finite volume method on right quadrangular prism grids
Journal of Computational and Applied Mathematics
Hierarchical error estimates for finite volume approximation solution of elliptic equations
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Superconvergent biquadratic finite volume element method for two-dimensional Poisson's equations
Journal of Computational and Applied Mathematics
A New Class of High Order Finite Volume Methods for Second Order Elliptic Equations
SIAM Journal on Numerical Analysis
Biquadratic finite volume element methods based on optimal stress points for parabolic problems
Journal of Computational and Applied Mathematics
Higher-order finite volume methods for elliptic boundary value problems
Advances in Computational Mathematics
A Family of Finite Volume Schemes of Arbitrary Order on Rectangular Meshes
Journal of Scientific Computing
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Locally conservative, finite volume-type methods based on continuous piecewise polynomial functions of degree r \ge 2 are introduced and analyzed in the context of indefinite elliptic problems in one space dimension. The new methods extend and generalize the classical finite volume method based on piecewise linear functions. We derive a priori error estimates in the L2, H1, and L^\infty norm and discuss superconvergence effects for the error and its derivative. Explicit, residual-based a posteriori error bounds in the L2 and energy norm are also derived. We compute the experimental order of convergence and show the results of an adaptive algorithm based on the a posteriori error estimates.