Results 11 to 20 of about 11,295 (169)
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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Mathematics, 2023 This study examined a Cauchy problem for a multi-dimensional Laplace equation with mixed boundary. This problem is severely ill-posed in the sense of Hadamard.
Xianli Lv, Xiufang Feng
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Identifying the Unknown Source in Linear Parabolic Equation by a Convoluting Equation Method
Mathematics, 2022 This article is devoted to identifying a space-dependent source term in linear parabolic equations. Such a problem is ill posed, i.e., a small perturbation in the input data may cause a dramatically large error in the solution (if it exists).
Zhenping Li +2 more
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A Posteriori Error Estimates for Darcy–Forchheimer’s Problem
Computational Methods in Applied Mathematics, 2022 Abstract This work deals with the a posteriori error estimates for the Darcy–Forchheimer problem. We first introduce the corresponding variational formulation for the nonlinear problem and discretize it by using the finite-element method.
Toni Sayah, Georges Semaan, Faouzi Triki
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A Posteriori Fractional Tikhonov Regularization Method for the Problem of Analytic Continuation
Mathematics, 2021 In this paper, the numerical analytic continuation problem is addressed and a fractional Tikhonov regularization method is proposed. The fractional Tikhonov regularization not only overcomes the difficulty of analyzing the ill-posedness of the ...
Xuemin Xue, Xiangtuan Xiong
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A Posteriori Error Estimates for the Generalized Overlapping Domain Decomposition Methods
Journal of Applied Mathematics, 2012 A posteriori error estimates for the generalized overlapping domain decomposition method (GODDM) (i.e., with Robin boundary conditions on the interfaces), for second order boundary value problems, are derived.
Hakima Benlarbi, Ahmed-Salah Chibi
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An adaptive algorithm for the transport equation with time dependent velocity
SN Applied Sciences, 2020 An a posteriori error estimate is derived for the approximation of the transport equation with a time dependent transport velocity. Continuous, piecewise linear, anisotropic finite elements are used for space discretization, the Crank-Nicolson scheme ...
Samuel Dubuis, Marco Picasso
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Verification of the ROSFOND/ABBN nuclear data based on the OECD/NEA benchmark on criticality safety of mox-fueled systems [PDF]
Nuclear Energy and Technology, 2019 The paper presents the results of a computational analysis of the OECD/NEA benchmark conducted to estimate the accuracy of the critical safety parameters of multiplying MOX-fueled systems.
Olga N. Andrianova +2 more
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Abstract and Applied Analysis, 2014 Explicit formulae of constants within the a posteriori error estimate for optimal control problems are investigated with Legendre-Galerkin spectral methods. The constrained set is put on the control variable.
Jianwei Zhou
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Parametric model-order-reduction development for unsteady convection
Frontiers in Physics, 2022 A time-averaged error indicator with POD-hGreedy is developed to drive parametric model order reduction (pMOR) for 2D unsteady natural convection in a high-aspect ratio slot parameterized with the Prandtl number, Rayleigh number, and slot angle with ...
Ping-Hsuan Tsai +2 more
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