In this paper we review some recent applications of the mimetic finite difference method to nonlinear problems (variational inequalities and quasilinear elliptic equations) and optimal control problems governed by linear elliptic partial differential equations. Several numerical examples show the effectiveness of mimetic finite differences in building accurate numerical approximations. Finally, driven by a real-world industrial application (the numerical simulation of the extrusion process) we explore possible further applications of the mimetic finite difference method to nonlinear Stokes equations and shape optimization/free-boundary problems. © 2014 World Scientific Publishing Company.

Antonietti, P., BEIRAO DA VEIGA, L., Bigoni, N., & Verani, M. (2014). Mimetic finite differences for nonlinear and control problems. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 24(8), 1457-1493 [10.1142/S0218202514400016].

Mimetic finite differences for nonlinear and control problems

BEIRAO DA VEIGA, LOURENCO
Secondo
;
2014

Abstract

In this paper we review some recent applications of the mimetic finite difference method to nonlinear problems (variational inequalities and quasilinear elliptic equations) and optimal control problems governed by linear elliptic partial differential equations. Several numerical examples show the effectiveness of mimetic finite differences in building accurate numerical approximations. Finally, driven by a real-world industrial application (the numerical simulation of the extrusion process) we explore possible further applications of the mimetic finite difference method to nonlinear Stokes equations and shape optimization/free-boundary problems. © 2014 World Scientific Publishing Company.
Articolo in rivista - Articolo scientifico
control problems; Mimetic finite differences; nonlinear problems; Applied Mathematics; Modeling and Simulation
English
1457
1493
37
Special Issue
Antonietti, P., BEIRAO DA VEIGA, L., Bigoni, N., & Verani, M. (2014). Mimetic finite differences for nonlinear and control problems. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 24(8), 1457-1493 [10.1142/S0218202514400016].
Antonietti, P; BEIRAO DA VEIGA, L; Bigoni, N; Verani, M
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/98403
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