On Finite Element Approximation of the Gradient for Solution of Poisson Equation
Neittaanmäki, P., Saranen, J. (1981). On Finite Element Approximation of the Gradient for Solution of Poisson Equation. Numerische Mathematik 37, 333-337. 10.1007/BF01400312
Published inNumerische Mathematik
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 assumption on triangulations is needed.
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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 (North-Holland, 1987)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 ...
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 ...
Finite element approximation for a div-rot system with mixed boundary conditions in non-smooth plane domains Křížek, Michal; Neittaanmäki, Pekka (Československá akademie věd. Matematický ústav., 1984)The authors examine a finite element method for the numerical approximation of the solution to a div-rot system with mixed boundary conditions in bounded plane domains with piecewise smooth boundary. The solvability of the ...