The virtual element method for a minimal surface problem

被引：0
作者：
Paola Francesca Antonietti
Silvia Bertoluzza
Daniele Prada
Marco Verani
机构：
[1] Politecnico di Milano,MOX, Dipartimento di Matematica
[2] Istituto di Matematica Applicata e Tecnologie Informatiche - CNR,undefined
来源：
Calcolo | 2020年 / 57卷
关键词：
Virtual element method; Minimal surface problem; Quasi-linear elliptic PDEs; 65N12; 65N30;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper we consider the Virtual Element discretization of a minimal surface problem, a quasi-linear elliptic partial differential equation modeling the problem of minimizing the area of a surface subject to a prescribed boundary condition. We derive an optimal error estimate and present several numerical tests assessing the validity of the theoretical results.
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  • [1] Beirão da Veiga L(2016)Preface [Special issue—Polyhedral discretization for PDE] ESAIM Math. Model. Numer. Anal. 50 633-634
  • [2] Ern A(2013)Basic principles of virtual element methods Math. Models Methods Appl. Sci. 23 199-214
  • [3] Beirão da Veiga L(2016)A SIAM J. Numer. Anal. 54 34-56
  • [4] Brezzi F(2018) virtual element method for the Cahn–Hilliard equation with polygonal meshes Calcolo 55 21-343
  • [5] Cangiani A(2018)A mixed virtual element method for a nonlinear Brinkman model of porous media flow SIAM J. Numer. Anal. 56 317-1242
  • [6] Manzini G(2018)A mixed virtual element method for quasi-Newtonian Stokes flows SIAM J. Numer. Anal. 56 1210-657
  • [7] Marini L(2017)Virtual elements for the Navier–Stokes problem on polygonal meshes Comput. Mech. 60 643-346
  • [8] Russo A(2015)Arbitrary order 2D virtual elements for polygonal meshes: part II, inelastic problem Comput. Methods Appl. Mech. Eng. 295 327-187
  • [9] Antonietti PF(2018)A virtual element method for elastic and inelastic problems on polytope meshes IMA J. Numer. Anal. 145 175-991
  • [10] Beirão da Veiga L(2019)Virtual element methods for the obstacle problem Appl. Numer. Math. 96 971-245
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