A Priori Error Estimates for the Optimal Control of the Integral Fractional Laplacian [PDF]
SIAM Journal on Control and Optimization, 2019 We design and analyze solution techniques for a linear-quadratic optimal control problem involving the integral fractional Laplacian. We derive existence and uniqueness results, first-order optimality conditions, and regularity estimates for the optimal variables.
Marta D'Elia +2 more
openaire +4 more sources
Bayesian updating: increasing sample size during the course of a study
BMC Medical Research Methodology, 2021 Background A priori sample size calculation requires an a priori estimate of the size of the effect. An incorrect estimate may result in a sample size that is too low to detect effects or that is unnecessarily high. An alternative to a priori sample size
Mirjam Moerbeek
doaj +1 more source
Goal-oriented adaptive method for Fredholm partial integro-differential equations
Ain Shams Engineering Journal, 2023 In this article, a goal-oriented adaptive scheme is proposed for Fredholm partial integro-differential equations (FPIDEs). The aim of this work is to obtain higher accuracy approximations for the unknown function and its derivative at a given fixed point.
M. Sameeh, A. Elsaid, M. El-Agamy
doaj +1 more source
Reconstructing the right-hand side of the Rayleigh–Stokes problem with nonlocal in time condition
Advances in Difference Equations, 2021 In this paper, the problem of finding the source function for the Rayleigh–Stokes equation is considered. According to Hadamard’s definition, the sought solution of this problem is both unstable and independent of continuous data. By using the fractional
Phuong Nguyen Duc +3 more
doaj +1 more source
Robust a priori and a posteriori error analysis for the approximation of Allen–Cahn and Ginzburg–Landau equations past topological changes [PDF]
, 2010 A priori and a posteriori error estimates are derived for the numerical approximation of scalar and complex valued phase field models. Particular attention is devoted to the dependence of the estimates on a small parameter and to the validity of the ...
Rüdiger Müller +12 more
core +1 more source
An H1 -Galerkin Mixed Finite Element Approximation of a Nonlocal Hyperbolic Equation
Mathematical Modelling and Analysis, 2017 In this paper we investigate a semi-discrete H1 -Galerkin mixed finite element approximation of one kind of nolocal second order nonlinear hyperbolic equation, which is often used to describe vibration of an elastic string.
Fengxin Chen, Zhaojie Zhou
doaj +1 more source
A priori and a posteriori analysis of the quasinonlocal quasicontinuum method in 1D [PDF]
, 2010 For a next-nearest neighbour pair interaction model in a periodic domain, a priori and a posteriori analyses of the quasinonlocal quasicontinuum method (QNL-QC) are presented.
Christoph Ortner, Ortner, Christoph
core +1 more source
A-priori estimates of the hp-adaptive BEM in elastic scattering of acoustic waves
Computer Assisted Methods in Engineering and Science, 2023 In the paper some a-priori hp-adaptive error estimates, applied to the problem of acoustic wave scattering on an elastic body in the 2D space, solved by the Boundary Element Method, are presented.
Andrzej Karafiat
doaj
Estimating the Position of an Image with Unknown Intensity Shape
Communications, 2021 The problem considered is to estimate the image position of a spatially extended object. It is assumed that the shape of the image intensity is a priori unknown, but it can be predicted with some error.
Yury E. Korchagin +3 more
doaj +1 more source
A priori error estimation for the stochastic perturbation method
Computer Methods in Applied Mechanics and Engineering, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Xiang-Yu +3 more
openaire +3 more sources