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Journal of Scientific Computing

Erschienen in:

27.10.2018

An Asymptotics-Based Adaptive Finite Element Method for Kohn–Sham Equation

verfasst von: Yedan Shen, Yang Kuang, Guanghui Hu

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2019

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Abstract

In Radovitzky and Ortiz (Comput Methods Appl Mech Eng 172(1–4):203–240, 1999), an error estimation technique for nonlinear PDEs is presented to adaptively generating mesh, based on the reduction of the order of the approximate polynomial. In this paper, following a similar analysis framework, we propose an a posteriori error estimation for Kohn–Sham equation by coarsening mesh. An upper bound for the difference of the total energies on two successively refined meshes is derived by the numerical solutions on two meshes through an asymptotic analysis, which finally generates an a posteriori error estimation. A variety of numerical tests show that such an a posteriori error estimation works very well in our h-adaptive finite element method framework. In addition, to further improve the efficiency, we solve a Poisson equation instead of the Kohn–Sham equation on the coarsened mesh. The effectiveness of this improvement is analyzed and numerically examined.

Vorheriger Artikel A Nonconforming Immersed Finite Element Method for Elliptic Interface Problems

Nächster Artikel Numerical Simulation and Error Estimation of the Time-Dependent Allen–Cahn Equation on Surfaces with Radial Basis Functions

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Titel: An Asymptotics-Based Adaptive Finite Element Method for Kohn–Sham Equation
verfasst von: Yedan Shen
Yang Kuang
Guanghui Hu
Publikationsdatum: 27.10.2018
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2019
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-018-0861-0

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