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We consider the finite volume element method for elliptic problems using isoparametric bilinear elements on quadrilateral meshes. A gradient recovery method is presented by using the patch interpolation technique. Based on some superclose estimates, we prove that the recovered gradient $R(\nabla u_h)$ possesses the superconvergence: $\|\nabla u-R(\nabla u_h)\|=O(h^2)\|u\|_3$. Finally, some numerical examples are provided to illustrate our theoretical analysis.
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참고문헌 (22)
참고문헌 신청
Z. Q. Cai / 1991 / On the finite volume element method / Numer. Math 58(7):713~735
L. Chen / 2010 / A new class of high order finite volume methods for second order elliptic equations / SIAM J. Numer. Anal 47(6):4021~4023
Z. Y. Chen / 1994 / L2 estimate of linear element generalized difference schemes / Acta. Sci. Nat. Univ. Sunyatseni 33:22~28
S. H. Chou / 2000 / Error estimates in L2, H1, L∞ in covolume methods for elliptic and parabolic problem: a unified approach / Math. Comp 69(229):103~120
P. G. Ciarlet / 1978 / The Finite ElementMethods for Elliptic Problems / North-Holland
L. Chen / 2010 / A new class of high order finite volume methods for second order elliptic equations / SIAM J. Numer. Anal 47(6):4021~4023
Z. Y. Chen / 1994 / L2 estimate of linear element generalized difference schemes / Acta. Sci. Nat. Univ. Sunyatseni 33:22~28
S. H. Chou / 2000 / Error estimates in L2, H1, L∞ in covolume methods for elliptic and parabolic problem: a unified approach / Math. Comp 69(229):103~120
P. G. Ciarlet / 1978 / The Finite ElementMethods for Elliptic Problems / North-Holland
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