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List of publications of Karel Segeth
Ljusternik acceleration and the extrapolated S.O.R. method
L∞(L2) and L∞(L∞) error estimates for mixed methods for integro-differential equations of parabolic type
Error estimates in L∞(0,T;L2(Ω)), L∞(0,T;L2(Ω)2), L∞(0,T;L∞(Ω)), L∞(0,T;L∞(Ω)2), Ω in , are derived for a mixed finite element method for the initial-boundary value problem for integro-differential equation based on the Raviart-Thomas space Vh x Wh ⊂ H(div;Ω) x L2(Ω). Optimal order estimates are obtained for the approximation of u,ut in L∞(0,T;L2(Ω)) and the associated velocity p in L∞(0,T;L2(Ω)2), divp in L∞(0,T;L2(Ω)). Quasi-optimal order estimates are obtained for the approximation...
Llist of participants
LMS-Newton adaptive filtering using FFT-based conjugate gradient iterations.
Local a posteriori estimates for the Stokes problem.
Local accuracy in finite element analysis using curved isoparametric elements
The finite element method (FEM) is popularly used for numerically approximating PDE(s) over complicated domains due to its rich mathematical background, versatility, and ease of implementation. In this article, we investigate one of its important features, i.e., the approximation of PDE(s) over nonpolygonal Lipschitz domains by higher-order simplicial elements in 2D and 3D. This important issue is not well understood and often ignored by engineers due to its mathematical complexity, i.e., the FEM...
Local analysis of a cubically convergent method for variational inclusions
This paper deals with variational inclusions of the form 0 ∈ φ(x) + F(x) where φ is a single-valued function admitting a second order Fréchet derivative and F is a set-valued map from to the closed subsets of . When a solution z̅ of the previous inclusion satisfies some semistability properties, we obtain local superquadratic or cubic convergent sequences.
Local and semilocal convergence theorems for Newton's method based on continuously Fréchet differentiable operators.
Local approximation estimators for algebraic multigrid.
Local behaviour of the derivative of a mid point cubic spline interpolator.
Local convergence analysis for a certain class of inexact methods.
Local Convergence Analysis for Partitioned Quasi-Newton Updates.
Local convergence analysis of a modified Newton-Jarratt's composition under weak conditions
A. Cordero et. al (2010) considered a modified Newton-Jarratt's composition to solve nonlinear equations. In this study, using decomposition technique under weaker assumptions we extend the applicability of this method. Numerical examples where earlier results cannot apply to solve equations but our results can apply are also given in this study.