An efficient numerical approach for stochastic evolution PDEs driven by random diffusion coefficients and multiplicative noise
In this paper, we investigate the stochastic evolution equations (SEEs) driven by a bounded log-Whittle-Mate´rn (W-M) random diffusion coefficient field and Q-Wiener multiplicative force noise. First, the well-posedness of the underlying equations is established by proving the existence, uniqueness,...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-09-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20221134?viewType=HTML |
| _version_ | 1797996602846085120 |
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| author | Xiao Qi Mejdi Azaiez Can Huang Chuanju Xu |
| author_facet | Xiao Qi Mejdi Azaiez Can Huang Chuanju Xu |
| author_sort | Xiao Qi |
| collection | DOAJ |
| description | In this paper, we investigate the stochastic evolution equations (SEEs) driven by a bounded log-Whittle-Mate´rn (W-M) random diffusion coefficient field and Q-Wiener multiplicative force noise. First, the well-posedness of the underlying equations is established by proving the existence, uniqueness, and stability of the mild solution. A sampling approach called approximation circulant embedding with padding is proposed to sample the random coefficient field. Then a spatio-temporal discretization method based on semi-implicit Euler-Maruyama scheme and finite element method is constructed and analyzed. An estimate for the strong convergence rate is derived. Numerical experiments are finally reported to confirm the theoretical result. |
| first_indexed | 2024-04-11T10:19:54Z |
| format | Article |
| id | doaj.art-df1583b26ac54175ba06053c3772227c |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-11T10:19:54Z |
| publishDate | 2022-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-df1583b26ac54175ba06053c3772227c2022-12-22T04:29:48ZengAIMS PressAIMS Mathematics2473-69882022-09-01712206842071010.3934/math.20221134An efficient numerical approach for stochastic evolution PDEs driven by random diffusion coefficients and multiplicative noiseXiao Qi 0Mejdi Azaiez1Can Huang2Chuanju Xu 31. School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High Performance Scientific Computing, Xiamen University, 361005 Xiamen, China1. School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High Performance Scientific Computing, Xiamen University, 361005 Xiamen, China 2. Bordeaux INP, Laboratoire I2M UMR 5295, 33607 Pessac, France1. School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High Performance Scientific Computing, Xiamen University, 361005 Xiamen, China1. School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High Performance Scientific Computing, Xiamen University, 361005 Xiamen, ChinaIn this paper, we investigate the stochastic evolution equations (SEEs) driven by a bounded log-Whittle-Mate´rn (W-M) random diffusion coefficient field and Q-Wiener multiplicative force noise. First, the well-posedness of the underlying equations is established by proving the existence, uniqueness, and stability of the mild solution. A sampling approach called approximation circulant embedding with padding is proposed to sample the random coefficient field. Then a spatio-temporal discretization method based on semi-implicit Euler-Maruyama scheme and finite element method is constructed and analyzed. An estimate for the strong convergence rate is derived. Numerical experiments are finally reported to confirm the theoretical result.https://www.aimspress.com/article/doi/10.3934/math.20221134?viewType=HTMLseesrandom coefficientq-wiener multiplicative noisestrong convergence |
| spellingShingle | Xiao Qi Mejdi Azaiez Can Huang Chuanju Xu An efficient numerical approach for stochastic evolution PDEs driven by random diffusion coefficients and multiplicative noise AIMS Mathematics sees random coefficient q-wiener multiplicative noise strong convergence |
| title | An efficient numerical approach for stochastic evolution PDEs driven by random diffusion coefficients and multiplicative noise |
| title_full | An efficient numerical approach for stochastic evolution PDEs driven by random diffusion coefficients and multiplicative noise |
| title_fullStr | An efficient numerical approach for stochastic evolution PDEs driven by random diffusion coefficients and multiplicative noise |
| title_full_unstemmed | An efficient numerical approach for stochastic evolution PDEs driven by random diffusion coefficients and multiplicative noise |
| title_short | An efficient numerical approach for stochastic evolution PDEs driven by random diffusion coefficients and multiplicative noise |
| title_sort | efficient numerical approach for stochastic evolution pdes driven by random diffusion coefficients and multiplicative noise |
| topic | sees random coefficient q-wiener multiplicative noise strong convergence |
| url | https://www.aimspress.com/article/doi/10.3934/math.20221134?viewType=HTML |
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