Convergence rates for diffusive shallow water equations (DSW) using higher order polynomials
In this paper, we describe the diffusive shallow water equation (DSW) and discuss a numerical strategy to solve it using the generalized-?? method as a method for temporal discretization. This method provides a good norm estimate of the error and guarantees an optimal convergence rate for the spatia...
| Main Authors: | , , , , , |
|---|---|
| Format: | Journal Article |
| Published: |
2012
|
| Online Access: | http://hdl.handle.net/20.500.11937/51503 |
| _version_ | 1848758714505363456 |
|---|---|
| author | Radwan, H. Vignal, P. Collier, N. Dalcin, L. Santillana, M. Calo, Victor |
| author_facet | Radwan, H. Vignal, P. Collier, N. Dalcin, L. Santillana, M. Calo, Victor |
| author_sort | Radwan, H. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we describe the diffusive shallow water equation (DSW) and discuss a numerical strategy to solve it using the generalized-?? method as a method for temporal discretization. This method provides a good norm estimate of the error and guarantees an optimal convergence rate for the spatial discretization. We also discuss the effect of higher polynomial orders on the convergence rates, focusing on the nonlinear DSW problem. Our numerical experiments show that optional convergence rates can be obtained for polynomial orders 1 through 4. |
| first_indexed | 2025-11-14T09:48:23Z |
| format | Journal Article |
| id | curtin-20.500.11937-51503 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:48:23Z |
| publishDate | 2012 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-515032017-03-24T11:53:45Z Convergence rates for diffusive shallow water equations (DSW) using higher order polynomials Radwan, H. Vignal, P. Collier, N. Dalcin, L. Santillana, M. Calo, Victor In this paper, we describe the diffusive shallow water equation (DSW) and discuss a numerical strategy to solve it using the generalized-?? method as a method for temporal discretization. This method provides a good norm estimate of the error and guarantees an optimal convergence rate for the spatial discretization. We also discuss the effect of higher polynomial orders on the convergence rates, focusing on the nonlinear DSW problem. Our numerical experiments show that optional convergence rates can be obtained for polynomial orders 1 through 4. 2012 Journal Article http://hdl.handle.net/20.500.11937/51503 restricted |
| spellingShingle | Radwan, H. Vignal, P. Collier, N. Dalcin, L. Santillana, M. Calo, Victor Convergence rates for diffusive shallow water equations (DSW) using higher order polynomials |
| title | Convergence rates for diffusive shallow water equations (DSW) using higher order polynomials |
| title_full | Convergence rates for diffusive shallow water equations (DSW) using higher order polynomials |
| title_fullStr | Convergence rates for diffusive shallow water equations (DSW) using higher order polynomials |
| title_full_unstemmed | Convergence rates for diffusive shallow water equations (DSW) using higher order polynomials |
| title_short | Convergence rates for diffusive shallow water equations (DSW) using higher order polynomials |
| title_sort | convergence rates for diffusive shallow water equations (dsw) using higher order polynomials |
| url | http://hdl.handle.net/20.500.11937/51503 |