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A posteriori error estimates of spectral method for nonlinear parabolic optimal control problem [PDF]
Journal of Inequalities and Applications, 2018 In this paper, we investigate the spectral approximation of optimal control problem governed by nonlinear parabolic equations. A spectral approximation scheme for the nonlinear parabolic optimal control problem is presented. We construct a fully discrete
Lin Li +4 more
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Oscillation in a posteriori error estimation [PDF]
Numerische Mathematik, 2021 AbstractIn a posteriori error analysis, the relationship between error and estimator is usually spoiled by so-called oscillation terms, which cannot be bounded by the error. In order to remedy, we devise a new approach where the oscillation has the following two properties.
Christian Kreuzer, Andreas Veeser
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Error estimates for approximating fixed points and best proximity points for noncyclic and cyclic contraction mappings [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2023 In this article, we find a priori and a posteriori error estimates of the fixed point for the Picard iteration associated with a noncyclic contraction map, which is defined on a uniformly convex Banach space with a modulus of convexity of power type.
A. Safari-Hafshejani
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ADAPTIVE SOLUTION OF THE NEUTRON DIFFUSION EQUATION WITH HETEROGENEOUS COEFFICIENTS USING THE MIXED FINITE ELEMENT METHOD ON STRUCTURED MESHES [PDF]
EPJ Web of Conferences, 2021 The neutron transport equation can be used to model the physics of the nuclear reactor core. Its solution depends on several variables and requires a lot of high precision computations.
Do Minh-Hieu +2 more
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مجلة بغداد للعلوم, 2021 The aim of this paper is to derive a posteriori error estimates for semilinear parabolic interface problems. More specifically, optimal order a posteriori error analysis in the - norm for semidiscrete semilinear parabolic interface problems is derived by
Younis Abid Sabawi
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A Priori and a Posteriori Error Analysis for Generic Linear Elliptic Problems
Tikrit Journal of Pure Science, 2022 In this paper, a priori error analysis has been examined for the continuous Galerkin finite element method which is used for solving a generic scalar and a generic system of linear elliptic equations.
Hala Raad, Mohammad Sabawi
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A Posteriori Error Estimation for the p-Curl Problem [PDF]
SIAM Journal on Numerical Analysis, 2020 We derive a posteriori error estimates for a semi-discrete finite element approximation of a nonlinear eddy current problem arising from applied superconductivity, known as the $p$-curl problem. In particular, we show the reliability for non-conforming Nédélec elements based on a residual type argument and a Helmholtz-Weyl decomposition of $W^p_0(\text{
Andy T. S. Wan, Marc Laforest
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A Posteriori Error Estimates for the Allen--Cahn Problem [PDF]
SIAM Journal on Numerical Analysis, 2020 This work is concerned with the proof of \emph{a posteriori} error estimates for fully-discrete Galerkin approximations of the Allen-Cahn equation in two and three spatial dimensions. The numerical method comprises of the backward Euler method combined with conforming finite elements in space.
Konstantinos Chrysafinos +2 more
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A posteriori error estimates for the Lindblad master equation [PDF]
QuantumWe are interested in the simulation of open quantum systems governed by the Lindblad master equation in an infinite-dimensional Hilbert space. To simulate the solution of this equation, the standard approach involves two sequential approximations: first,
Paul-Louis Etienney +2 more
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A posteriori error estimates based on superconvergence of FEM for fractional evolution equations
Open Mathematics, 2021 In this paper, we consider an approximation scheme for fractional evolution equation with variable coefficient. The space derivative is approximated by triangular finite element and the time fractional derivative is evaluated by the L1 approximation. The
Tang Yuelong, Hua Yuchun
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