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.
引用
收藏
相关论文
共 50 条
  • [1] The virtual element method for a minimal surface problem
    Antonietti, Paola Francesca
    Bertoluzza, Silvia
    Prada, Daniele
    Verani, Marco
    CALCOLO, 2020, 57 (04)
  • [2] A virtual element method for the transmission eigenvalue problem
    Mora, David
    Velasquez, Ivan
    MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2018, 28 (14): : 2803 - 2831
  • [3] A mixed virtual element method for the Brinkman problem
    Caceres, Ernesto
    Gatica, Gabriel N.
    Sequeira, Filander A.
    MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2017, 27 (04): : 707 - 743
  • [4] A virtual element method for the acoustic vibration problem
    Beirao da Veiga, Lourenco
    Mora, David
    Rivera, Gonzalo
    Rodriguez, Rodolfo
    NUMERISCHE MATHEMATIK, 2017, 136 (03) : 725 - 763
  • [5] Virtual element method for simplified friction problem
    Wang, Fei
    Wei, Huayi
    APPLIED MATHEMATICS LETTERS, 2018, 85 : 125 - 131
  • [6] A virtual element method for the acoustic vibration problem
    Lourenço Beirão da Veiga
    David Mora
    Gonzalo Rivera
    Rodolfo Rodríguez
    Numerische Mathematik, 2017, 136 : 725 - 763
  • [7] A virtual element method for the Steklov eigenvalue problem
    Mora, David
    Rivera, Gonzalo
    Rodriguez, Rodolfo
    MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2015, 25 (08): : 1421 - 1445
  • [8] A posteriori virtual element method for the acoustic vibration problem
    Lepe, F.
    Mora, D.
    Rivera, G.
    Velasquez, I.
    ADVANCES IN COMPUTATIONAL MATHEMATICS, 2023, 49 (01)
  • [9] A nonconforming Trefftz virtual element method for the Helmholtz problem
    Mascotto, Lorenzo
    Perugia, Ilaria
    Pichler, Alexander
    MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2019, 29 (09): : 1619 - 1656
  • [10] THE INTERIOR PENALTY VIRTUAL ELEMENT METHOD FOR THE BIHARMONIC PROBLEM
    Zhao, Jikun
    Mao, Shipeng
    Zhang, Bei
    Wang, Fei
    MATHEMATICS OF COMPUTATION, 2023, 92 (342) : 1543 - 1574
12345