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International Journal of Computer Mathematics Volume 96, 2019 - Issue 5
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Original Article

Virtual element method for semilinear hyperbolic problems on polygonal meshes

Dibyendu AdakDepartment of Mathematics, Indian Institute of Space Science and Technology, Thiruvananthapuram, Kerala
,
E. NatarajanDepartment of Mathematics, Indian Institute of Space Science and Technology, Thiruvananthapuram, Kerala
&
Sarvesh KumarDepartment of Mathematics, Indian Institute of Space Science and Technology, Thiruvananthapuram, Kerala;Department of Mathematics, Indian Institute of Space Science and Technology, Thiruvananthapuram, KeralaCorrespondence[email protected]
Pages 971-991 | Received 26 Oct 2017, Accepted 30 Apr 2018, Published online: 01 Jun 2018

Citations (29)

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M. Arrutselvi & E. Natarajan. (2021) Virtual element method for nonlinear convection–diffusion–reaction equation on polygonal meshes. International Journal of Computer Mathematics 98:9, pages 1852-1876.
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Articles from other publishers (28)

Yu-jie Huang, Zhi-shan Zheng, Feng Yao, Chen Zeng, Hui Zhang, Sundararajan Natarajan & Shi-lang Xu. (2024) Arbitrary polygon-based CSFEM-PFCZM for quasi-brittle fracture of concrete. Computer Methods in Applied Mechanics and Engineering 424, pages 116899.
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Sudheer Mishra & E. Natarajan. (2023) Local projection stabilization virtual element method for the convection-diffusion equation with nonlinear reaction term. Computers & Mathematics with Applications 152, pages 181-198.
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Wanxiang Liu, Yanping Chen, Qiling Gu & Yunqing Huang. (2023) Virtual element method for nonlinear Sobolev equation on polygonal meshes. Numerical Algorithms 94:4, pages 1731-1761.
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Sudheer Mishra & E. Natarajan. (2023) A streamline-derivative-based local projection stabilization virtual element method for nonlinear convection–diffusion–reaction equation. Calcolo 60:4.
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M. Arrutselvi & E. Natarajan. (2023) Virtual element stabilization for the system of time-dependent nonlinear convection-diffusion-reaction equations. Computers & Mathematics with Applications 142, pages 121-139.
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Yang Xu, Zhenguo Zhou & Jingjun Zhao. (2023) Error Estimates of Conforming Virtual Element Methods with a Modified Symmetric Nitsche’s Formula for 2D Semilinear Parabolic Equations. Journal of Scientific Computing 95:3.
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Buying Zhang, Jikun Zhao & Shaochun Chen. (2022) Virtual element method for the Sobolev equations. Mathematical Methods in the Applied Sciences 46:1, pages 1266-1281.
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Nitesh Verma & Sarvesh Kumar. (2023) VIRTUAL ELEMENT APPROXIMATIONS FOR NON-STATIONARY NAVIER-STOKES EQUATIONS ON POLYGONAL MESHES. Journal of Applied Analysis & Computation 13:3, pages 1155-1177.
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M. Arrutselvi, E. Natarajan & S. Natarajan. (2022) Virtual element method for the quasilinear convection-diffusion-reaction equation on polygonal meshes. Advances in Computational Mathematics 48:6.
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Liuchao Xiao, Meng Zhou & Jikun Zhao. (2022) The nonconforming virtual element method for semilinear elliptic problems. Applied Mathematics and Computation 433, pages 127402.
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Yang Xu, Zhenguo Zhou & Jingjun Zhao. (2022) Conforming Virtual Element Methods for Sobolev Equations. Journal of Scientific Computing 93:1.
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Jai Tushar, Anil Kumar & Sarvesh Kumar. (2022) Virtual element methods for general linear elliptic interface problems on polygonal meshes with small edges. Computers & Mathematics with Applications 122, pages 61-75.
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Sergio A. Gómez. (2022) High-order interpolatory Serendipity Virtual Element Method for semilinear parabolic problems. Calcolo 59:3.
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M. Arrutselvi, D. Adak, E. Natarajan, S. Roy & S. Natarajan. (2022) Virtual element analysis of nonlocal coupled parabolic problems on polygonal meshes. Calcolo 59:2.
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Jai Tushar, Anil Kumar & Sarvesh Kumar. (2022) Variational and Virtual Discretizations of Optimal Control Problems Governed by Diffusion Problems. Applied Mathematics & Optimization 85:2.
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Jai Tushar, Anil Kumar & Sarvesh Kumar. (2022) Approximations of Quasi-Linear Elliptic Optimal Control Problems on Polygonal Meshes Under Variational and Virtual Discretizations. International Journal of Applied and Computational Mathematics 8:1.
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Dibyendu Adak, M. Arrutselvi, E. Natarajan & S. Natarajan. 2022. The Virtual Element Method and its Applications. The Virtual Element Method and its Applications 59 91 .
N. Verma & S. Kumar. (2021) Lowest order virtual element approximations for transient Stokes problem on polygonal meshes. Calcolo 58:4.
Crossref
M. Arrutselvi & E. Natarajan. (2021) Virtual Element Method for Nonlinear Time-Dependent Convection-Diffusion-Reaction Equation. Computational Mathematics and Modeling 32:3, pages 376-386.
Crossref
M. Arrutselvi & E. Natarajan. (2021) Virtual element stabilization of convection-diffusion equation with shock capturing. Journal of Physics: Conference Series 1850:1, pages 012001.
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Dibyendu Adak & Sundararajan Natarajan. (2020) On the $${ H}^{1}$$ Conforming Virtual Element Method for Time Dependent Stokes Equation. Mathematics in Computer Science 15:1, pages 135-154.
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Paola Francesca Antonietti, Silvia Bertoluzza, Daniele Prada & Marco Verani. (2020) The virtual element method for a minimal surface problem. Calcolo 57:4.
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D. Adak & S. Natarajan. (2020) Virtual element methods for nonlocal parabolic problems on general type of meshes. Advances in Computational Mathematics 46:5.
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D. Adak & S. Natarajan. (2020) Virtual element method for semilinear sine–Gordon equation over polygonal mesh using product approximation technique. Mathematics and Computers in Simulation 172, pages 224-243.
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D. Adak & S. Natarajan. (2020) Virtual element method for a nonlocal elliptic problem of Kirchhoff type on polygonal meshes. Computers & Mathematics with Applications 79:10, pages 2856-2871.
Crossref
Kyoungsoo Park, Heng Chi & Glaucio H. Paulino. (2019) Numerical recipes for elastodynamic virtual element methods with explicit time integration. International Journal for Numerical Methods in Engineering 121:1, pages 1-31.
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Kyoungsoo Park, Heng Chi & Glaucio H. Paulino. (2019) On nonconvex meshes for elastodynamics using virtual element methods with explicit time integration. Computer Methods in Applied Mechanics and Engineering 356, pages 669-684.
Crossref
D. Adak, S. Natarajan & E. Natarajan. (2019) Virtual element method for semilinear elliptic problems on polygonal meshes. Applied Numerical Mathematics 145, pages 175-187.
Crossref

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