A virtual element method for the quasilinear equation −div(κ(u)gradu)=f using general polygonal and polyhedral meshes is presented and analysed. The nonlinear coefficient is evaluated with the piecewise polynomial projection of the virtual element ansatz. Well posedness of the discrete problem and optimal-order a priori error estimates in the H1- and L2-norm are proven. In addition, the convergence of fixed-point iterations for the resulting nonlinear system is established. Numerical tests confirm the optimal convergence properties of the method on general meshes.

Virtual element method for quasilinear elliptic problems / Cangiani, A.; Chatzipantelidis, P.; Diwan, G.; Georgoulis, E. H.. - In: IMA JOURNAL OF NUMERICAL ANALYSIS. - ISSN 0272-4979. - 40:4(2020), pp. 2450-2472. [10.1093/IMANUM/DRZ035]

Virtual element method for quasilinear elliptic problems

Cangiani A.
;
2020-01-01

Abstract

A virtual element method for the quasilinear equation −div(κ(u)gradu)=f using general polygonal and polyhedral meshes is presented and analysed. The nonlinear coefficient is evaluated with the piecewise polynomial projection of the virtual element ansatz. Well posedness of the discrete problem and optimal-order a priori error estimates in the H1- and L2-norm are proven. In addition, the convergence of fixed-point iterations for the resulting nonlinear system is established. Numerical tests confirm the optimal convergence properties of the method on general meshes.
2020
40
4
2450
2472
10.1093/IMANUM/DRZ035
https://academic.oup.com/imajna/article/40/4/2450/5586239
https://arxiv.org/abs/1707.01592
Cangiani, A.; Chatzipantelidis, P.; Diwan, G.; Georgoulis, E. H.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/128791
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