Displaying similar documents to “On a superconvergent finite element scheme for elliptic systems. III. Optimal interior estimates”

Finite element analysis of primal and dual variational formulations of semicoercive elliptic problems with nonhomogeneous obstacles on the boundary

Van Bon Tran (1988)

Aplikace matematiky

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The Poisson equation with non-homogeneous unilateral condition on the boundary is solved by means of finite elements. The primal variational problem is approximated on the basis of linear triangular elements, and O ( h ) -convergence is proved provided the exact solution is regular enough. For the dual problem piecewise linear divergence-free approximations are employed and O ( h 3 / 2 ) -convergence proved for a regular solution. Some a posteriori error estimates are also presented.

Shape optimization by means of the penalty method with extrapolation

Ivan Hlaváček (1994)

Applications of Mathematics

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A model shape optimal design in ℝ 2 is solved by means of the penalty method with extrapolation, which enables to obtain high order approximations of both the state function and the boundary flux, thus offering a reliable gradient for the sensitivity analysis. Convergence of the proposed method is proved for certain subsequences of approximate solutions.

Finite element analysis for unilateral problems with obstacles on the boundary

Jaroslav Haslinger (1977)

Aplikace matematiky

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Finite element analysis of unilateral problems with obstacles on the boundary is given. Provided the exact solution is smooth enough, we obtain the rate of convergence 0 ( h ) for the case of one and two (lower and upper) obstacles on the boundary. At the end of this paper the proof of convergence without any regularity assumptions on the exact solution u is given.

Error estimates for the numerical approximation of semilinear elliptic control problems with finitely many state constraints

Eduardo Casas (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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The goal of this paper is to derive some error estimates for the numerical discretization of some optimal control problems governed by semilinear elliptic equations with bound constraints on the control and a finitely number of equality and inequality state constraints. We prove some error estimates for the optimal controls in the L ∞ norm and we also obtain error estimates for the Lagrange multipliers associated to the state constraints as well as for the optimal states and optimal adjoint...

Postprocessing of a finite volume element method for semilinear parabolic problems

Min Yang, Chunjia Bi, Jiangguo Liu (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper, we study a postprocessing procedure for improving accuracy of the finite volume element approximations of semilinear parabolic problems. The procedure amounts to solve a source problem on a coarser grid and then solve a linear elliptic problem on a finer grid after the time evolution is finished. We derive error estimates in the and norms for the standard finite volume element scheme and an improved error estimate in the ...