On the Accuracy of the Finite Volume Element Method Based on Piecewise Linear Polynomials

Authors:
Richard E. Ewing;Tao Lin;Yanping Lin
Affiliations:
-;-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2001

Citing 0
Cited 28

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A mixed finite element method for nearly incompressible elasticity and Stokes equations using primal and dual meshes with quadrilateral and hexahedral grids

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Abstract

We present a general error estimation framework for a finite volume element (FVE) method based on linear polynomials for solving second-order elliptic boundary value problems. This framework treats the FVE method as a perturbation of the Galerkin finite element method and reveals that regularities in both the exact solution and the source term can affect the accuracy of FVE methods. In particular, the error estimates and counterexamples in this paper will confirm that the FVE method cannot have the standard O(h2) convergence rate in the L2 norm when the source term has the minimum regularity, only being in L2, even if the exact solution is in H2.