A priori and a posteriori error analysis for semilinear problems in liquid crystals
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Date
2023-11-01
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Language
en
Pages
50
3201-3250
3201-3250
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ESAIM: Mathematical Modelling and Numerical Analysis, Volume 57, issue 6
Abstract
In this paper, we develop a unified framework for the a priori and a posteriori error control of different lowest-order finite element methods for approximating the regular solutions of systems of partial differential equations under a set of hypotheses. The systems involve cubic nonlinearities in lower order terms, non-homogeneous Dirichlet boundary conditions, and the results are established under minimal regularity assumptions on the exact solution. The key contributions include (i) results for existence and local uniqueness of the discrete solutions using Newton Kantorovich theorem, (ii) a priori error estimates in the energy norm, and (iii) a posteriori error estimates that steer the adaptive refinement process. The results are applied to conforming, Nitsche, discontinuous Galerkin, and weakly over penalized symmetric interior penalty schemes for variational models of ferronematics and nematic liquid crystals. The theoretical estimates are corroborated by substantive numerical results.Description
Publisher Copyright: © 2023 Authors. All rights reserved.
Keywords
A priori and a posteriori, Conforming FEM Nitsche's method, Discontinuous Galerkin and WOPSIP methods, Error analysis, Ferronematics, Nematic liquid crystals, Non-homogeneous Dirichlet boundary conditions, Non-linear elliptic PDEs
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Citation
Maity, R R, Majumdar, A & Nataraj, N 2023, ' A priori and a posteriori error analysis for semilinear problems in liquid crystals ', ESAIM: Mathematical Modelling and Numerical Analysis, vol. 57, no. 6, pp. 3201-3250 . https://doi.org/10.1051/m2an/2023056