Details
| Original language | English |
|---|---|
| Pages (from-to) | 2279-2294 |
| Number of pages | 16 |
| Journal | Applicable analysis |
| Volume | 101 |
| Issue number | 6 |
| Publication status | Published - 26 Aug 2020 |
Abstract
In this work, we develop a Legendre spectral element method (LSEM) for solving the stochastic nonlinear system of advection–reaction–diffusion models. The used basis functions are based on a class of Legendre functions such that their mass and diffuse matrices are tridiagonal and diagonal, respectively. The temporal variable is discretized by a Crank–Nicolson finite-difference formulation. In the stochastic direction, we also employ a random variable W based on the Q-Wiener process. We inspect the rate of convergence and the unconditional stability for the achieved semi-discrete formulation. Then, the Legendre spectral element technique is used to obtain a full-discrete scheme. The error estimation of the proposed numerical scheme is substantiated based upon the energy method. The numerical results confirm the theoretical analysis.
Keywords
- error estimate, Nonlinear system of advection–reaction–diffusion equation, spectral element method (SEM), stochastic PDEs
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Applicable analysis, Vol. 101, No. 6, 26.08.2020, p. 2279-2294.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Legendre spectral element method (LSEM) to simulate the two-dimensional system of nonlinear stochastic advection–reaction–diffusion models
AU - Abbaszadeh, Mostafa
AU - Dehghan, Mehdi
AU - Khodadadian, Amirreza
AU - Wick, Thomas
N1 - Funding Information: The authors are grateful to the reviewers for carefully reading this paper and for their comments and suggestions which have improved the paper.
PY - 2020/8/26
Y1 - 2020/8/26
N2 - In this work, we develop a Legendre spectral element method (LSEM) for solving the stochastic nonlinear system of advection–reaction–diffusion models. The used basis functions are based on a class of Legendre functions such that their mass and diffuse matrices are tridiagonal and diagonal, respectively. The temporal variable is discretized by a Crank–Nicolson finite-difference formulation. In the stochastic direction, we also employ a random variable W based on the Q-Wiener process. We inspect the rate of convergence and the unconditional stability for the achieved semi-discrete formulation. Then, the Legendre spectral element technique is used to obtain a full-discrete scheme. The error estimation of the proposed numerical scheme is substantiated based upon the energy method. The numerical results confirm the theoretical analysis.
AB - In this work, we develop a Legendre spectral element method (LSEM) for solving the stochastic nonlinear system of advection–reaction–diffusion models. The used basis functions are based on a class of Legendre functions such that their mass and diffuse matrices are tridiagonal and diagonal, respectively. The temporal variable is discretized by a Crank–Nicolson finite-difference formulation. In the stochastic direction, we also employ a random variable W based on the Q-Wiener process. We inspect the rate of convergence and the unconditional stability for the achieved semi-discrete formulation. Then, the Legendre spectral element technique is used to obtain a full-discrete scheme. The error estimation of the proposed numerical scheme is substantiated based upon the energy method. The numerical results confirm the theoretical analysis.
KW - error estimate
KW - Nonlinear system of advection–reaction–diffusion equation
KW - spectral element method (SEM)
KW - stochastic PDEs
UR - http://www.scopus.com/inward/record.url?scp=85089866943&partnerID=8YFLogxK
U2 - 10.1080/00036811.2020.1807007
DO - 10.1080/00036811.2020.1807007
M3 - Article
AN - SCOPUS:85089866943
VL - 101
SP - 2279
EP - 2294
JO - Applicable analysis
JF - Applicable analysis
SN - 0003-6811
IS - 6
ER -