On a global superconvergence of the gradient of linear triangular elements
Křižek, M., Neittaanmäki, P. (1987). On a global superconvergence of the gradient of linear triangular elements. Journal of Computational and Applied Mathematics, 18 (2), 221-233. doi:10.1016/0377-0427(87)90018-5
Published inJournal of Computational and Applied Mathematics
© the Authors & North-Holland
We study a simple superconvergent scheme which recovers the gradient when solving a second-order elliptic problem in the plane by the usual linear elements. The recovered gradient globally approximates the true gradient even by one order of accuracy higher in the L2-norm than the piecewise constant gradient of the Ritz—Galerkin solution. A superconvergent approximation to the boundary flux is presented as well.
MetadataShow full item record
Showing items with similar title or keywords.
Neittaanmäki, Pekka; Křižek, Michal (Friedr. Vieweg & Sohn, 1987)In this contribution we first give a brief survey of postprocessing techniques for accelerating the convergence of finite element schemes for elliptic problems. We also generalize a local superconvergence technique recently ...
Neittaanmäki, Pekka; Saranen, Jukka (Springer, 1981)A nonconforming mixed finite element method is presented for approximation of ∇w with Δw=f,w| r =0. Convergence of the order∥∇w−uh∥0,Ω=O(h2) is proved, when linear finite elements are used. Only the standard regularity ...
On different finite element methods for approximating the gradient of the solution to the helmholtz equation Haslinger, Jaroslav; Neittaanmäki, Pekka (North-Holland, 1984)We consider the numerical solution of the Helmholtz equation by different finite element methods. In particular, we are interested in finding an efficient method for approximating the gradient of the solution. We first ...
Křižek, Michal; Neittaanmäki, Pekka (Springer, 1984)We study a superconvergence phenomenon which can be obtained when solving a 2nd order elliptic problem by the usual linear elements. The averaged gradient is a piecewise linear continuous vector field, the value of which ...
Lasiecka, I.; Sokołowski, J.; Neittaanmäki, Pekka (Polish Academy of Sciences, Institute of Mathematics, 1990)A numerical method for solving the wave equation with nonhomogenuous, nonsmooth Dirichlet boundary condition is proposed. Convergence of the method is proved and some erràr estimates are derived [L-S-2]. The method ...