An implicit midpoint spectral approximation of nonlocal Cahn--Hilliard equations
The paper is concerned with the convergence analysis of a numerical method for nonlocal Cahn--Hilliard equations. The temporal discretization is based on the implicit midpoint rule and a Fourier spectral discretization is used with respect to the spatial variables. The sequence of numerical approxim...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Society for Industrial and Applied Mathematics
2014
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| _version_ | 1826259890662801408 |
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| author | Benesova, B Melcher, C Süli, E |
| author_facet | Benesova, B Melcher, C Süli, E |
| author_sort | Benesova, B |
| collection | OXFORD |
| description | The paper is concerned with the convergence analysis of a numerical method for nonlocal Cahn--Hilliard equations. The temporal discretization is based on the implicit midpoint rule and a Fourier spectral discretization is used with respect to the spatial variables. The sequence of numerical approximations in shown to be bounded in various norms, uniformly with respect to the discretization parameters, and optimal order bounds on the global error of the scheme are derived. The uniform bounds on the sequence of numerical solutions as well as the error bounds hold unconditionally, in the sense that no restriction on the size of the time step in terms of the spatial discretization parameter needs to be assumed. |
| first_indexed | 2024-03-06T18:56:58Z |
| format | Journal article |
| id | oxford-uuid:122bbeab-86f5-4cda-ad8e-dea62cee9c60 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T18:56:58Z |
| publishDate | 2014 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:122bbeab-86f5-4cda-ad8e-dea62cee9c602022-03-26T10:06:22ZAn implicit midpoint spectral approximation of nonlocal Cahn--Hilliard equationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:122bbeab-86f5-4cda-ad8e-dea62cee9c60EnglishSymplectic Elements at OxfordSociety for Industrial and Applied Mathematics2014Benesova, BMelcher, CSüli, EThe paper is concerned with the convergence analysis of a numerical method for nonlocal Cahn--Hilliard equations. The temporal discretization is based on the implicit midpoint rule and a Fourier spectral discretization is used with respect to the spatial variables. The sequence of numerical approximations in shown to be bounded in various norms, uniformly with respect to the discretization parameters, and optimal order bounds on the global error of the scheme are derived. The uniform bounds on the sequence of numerical solutions as well as the error bounds hold unconditionally, in the sense that no restriction on the size of the time step in terms of the spatial discretization parameter needs to be assumed. |
| spellingShingle | Benesova, B Melcher, C Süli, E An implicit midpoint spectral approximation of nonlocal Cahn--Hilliard equations |
| title | An implicit midpoint spectral approximation of nonlocal Cahn--Hilliard equations |
| title_full | An implicit midpoint spectral approximation of nonlocal Cahn--Hilliard equations |
| title_fullStr | An implicit midpoint spectral approximation of nonlocal Cahn--Hilliard equations |
| title_full_unstemmed | An implicit midpoint spectral approximation of nonlocal Cahn--Hilliard equations |
| title_short | An implicit midpoint spectral approximation of nonlocal Cahn--Hilliard equations |
| title_sort | implicit midpoint spectral approximation of nonlocal cahn hilliard equations |
| work_keys_str_mv | AT benesovab animplicitmidpointspectralapproximationofnonlocalcahnhilliardequations AT melcherc animplicitmidpointspectralapproximationofnonlocalcahnhilliardequations AT sulie animplicitmidpointspectralapproximationofnonlocalcahnhilliardequations AT benesovab implicitmidpointspectralapproximationofnonlocalcahnhilliardequations AT melcherc implicitmidpointspectralapproximationofnonlocalcahnhilliardequations AT sulie implicitmidpointspectralapproximationofnonlocalcahnhilliardequations |