What is the smallest possible constant in Céa's lemma?

Wei Chen; Michal Křížek

Displaying similar documents to “What is the smallest possible constant in Céa's lemma?”

Optimal convergence and a posteriori error analysis of the original DG method for advection-reaction equations

Tie Zhu Zhang, Shu Hua Zhang (2015)

Applications of Mathematics

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We consider the original DG method for solving the advection-reaction equations with arbitrary velocity in $d$ space dimensions. For triangulations satisfying the flow condition, we first prove that the optimal convergence rate is of order $k + 1$ in the $L_{2}$ -norm if the method uses polynomials of order $k$ . Then, a very simple derivative recovery formula is given to produce an approximation to the derivative in the flow direction which superconverges with order $k + 1$ . Further we consider a residual-based...

A second-order finite volume element method on quadrilateral meshes for elliptic equations

Min Yang (2006)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In this paper, by use of affine biquadratic elements, we construct and analyze a finite volume element scheme for elliptic equations on quadrilateral meshes. The scheme is shown to be of second-order in $H^{1}$ -norm, provided that each quadrilateral in partition is almost a parallelogram. Numerical experiments are presented to confirm the usefulness and efficiency of the method.

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.

On mixed finite element techniques for elliptic problems.

Noor, M.Aslam (1983)

International Journal of Mathematics and Mathematical Sciences

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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 $L^{\infty}$ 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...

Superconvergence estimates of finite element methods for American options

Qun Lin, Tang Liu, Shu Hua Zhang (2009)

Applications of Mathematics

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In this paper we are concerned with finite element approximations to the evaluation of American options. First, following W. Allegretto etc., SIAM J. Numer. Anal. (2001), 834–857, we introduce a novel practical approach to the discussed problem, which involves the exact reformulation of the original problem and the implementation of the numerical solution over a very small region so that this algorithm is very rapid and highly accurate. Secondly by means of a superapproximation and...