Details
| Original language | English |
|---|---|
| Pages (from-to) | 12500-12521 |
| Number of pages | 22 |
| Journal | Mathematical Methods in the Applied Sciences |
| Volume | 44 |
| Issue number | 17 |
| Early online date | 2 Jul 2021 |
| Publication status | Published - 7 Nov 2021 |
Abstract
This paper is concerned with the numerical approximation of the solution of the coupled wave equation of Kirchhoff type with nonlinear boundary damping and memory term using a mixed finite element method. The Raviart-Thomas mixed finite element method is one of the most prominent techniques to discretize the second-order wave equations; therefore, we apply this scheme for space discretization. Furthermore, an L2-in-space error estimate is presented for this mixed finite element approximation. Finally, the efficiency of the method is verified by a numerical example.
Keywords
- 65N15 error bounds for boundary value problems involving PDEs, 65N22 Numerical solution of discretized equations for boundary value problems involving PDEs, convergence, nonlinear wave equation, Raviart-Thomas mixed finite element, semi-discretization
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
- Engineering(all)
- General Engineering
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In: Mathematical Methods in the Applied Sciences, Vol. 44, No. 17, 07.11.2021, p. 12500-12521.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A mixed finite element method for solving coupled wave equation of Kirchhoff type with nonlinear boundary damping and memory term
AU - Parvizi, Maryam
AU - Khodadadian, Amirreza
AU - Eslahchi, M. R.
N1 - Funding Information: M. Parvizi acknowledges support by the Deutsche Forschungsgemeinschaft (DFG) under Germany's Excellence Strategy within the Cluster of Excellence PhoenixD (EXC 2122, Project ID 390833453). She is also supported financially by FWF (Austrian Science Fund) Project No. P28367‐N35. Furthermore, the authors appreciate the useful comments given by the anonymous reviewers. Open access funding enabled and organized by Projekt DEAL.
PY - 2021/11/7
Y1 - 2021/11/7
N2 - This paper is concerned with the numerical approximation of the solution of the coupled wave equation of Kirchhoff type with nonlinear boundary damping and memory term using a mixed finite element method. The Raviart-Thomas mixed finite element method is one of the most prominent techniques to discretize the second-order wave equations; therefore, we apply this scheme for space discretization. Furthermore, an L2-in-space error estimate is presented for this mixed finite element approximation. Finally, the efficiency of the method is verified by a numerical example.
AB - This paper is concerned with the numerical approximation of the solution of the coupled wave equation of Kirchhoff type with nonlinear boundary damping and memory term using a mixed finite element method. The Raviart-Thomas mixed finite element method is one of the most prominent techniques to discretize the second-order wave equations; therefore, we apply this scheme for space discretization. Furthermore, an L2-in-space error estimate is presented for this mixed finite element approximation. Finally, the efficiency of the method is verified by a numerical example.
KW - 65N15 error bounds for boundary value problems involving PDEs
KW - 65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
KW - convergence
KW - nonlinear wave equation
KW - Raviart-Thomas mixed finite element
KW - semi-discretization
UR - http://www.scopus.com/inward/record.url?scp=85109015420&partnerID=8YFLogxK
U2 - 10.1002/mma.7556
DO - 10.1002/mma.7556
M3 - Article
AN - SCOPUS:85109015420
VL - 44
SP - 12500
EP - 12521
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
SN - 0170-4214
IS - 17
ER -