Spectral approximation of the H-1 gradient flow of a multi-well potential with bending energy
We consider a fully discrete approximation of the H1 gradient flow of an energy integral where the energy density is given by the sum of a nonnegative multi-well potential term and a bending energy term. The spatial discretization is based on a Fourier spectral method, which is combined with an impl...
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| Format: | Journal article |
| Language: | English |
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Department of Mathematics, University of Osijek
2014
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| _version_ | 1826282350563033088 |
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| author | Süli, E |
| author_facet | Süli, E |
| author_sort | Süli, E |
| collection | OXFORD |
| description | We consider a fully discrete approximation of the H1 gradient flow of an energy integral where the energy density is given by the sum of a nonnegative multi-well potential term and a bending energy term. The spatial discretization is based on a Fourier spectral method, which is combined with an implicit Euler time discretization. The numerical method is shown to be stable and to exhibit optimal orders of convergence with respect to its spatial and temporal discretization parameters in the ℓ∞ (0, T; H1) and ℓ∞ (0, T; L2) norms, without any limitations on the size of the time step in terms of the spatial discretization parameter. |
| first_indexed | 2024-03-07T00:42:31Z |
| format | Journal article |
| id | oxford-uuid:838d6744-efd4-4907-b144-c1d92ad5001b |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:42:31Z |
| publishDate | 2014 |
| publisher | Department of Mathematics, University of Osijek |
| record_format | dspace |
| spelling | oxford-uuid:838d6744-efd4-4907-b144-c1d92ad5001b2022-03-26T21:44:52ZSpectral approximation of the H-1 gradient flow of a multi-well potential with bending energyJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:838d6744-efd4-4907-b144-c1d92ad5001bEnglishSymplectic Elements at OxfordDepartment of Mathematics, University of Osijek2014Süli, EWe consider a fully discrete approximation of the H1 gradient flow of an energy integral where the energy density is given by the sum of a nonnegative multi-well potential term and a bending energy term. The spatial discretization is based on a Fourier spectral method, which is combined with an implicit Euler time discretization. The numerical method is shown to be stable and to exhibit optimal orders of convergence with respect to its spatial and temporal discretization parameters in the ℓ∞ (0, T; H1) and ℓ∞ (0, T; L2) norms, without any limitations on the size of the time step in terms of the spatial discretization parameter. |
| spellingShingle | Süli, E Spectral approximation of the H-1 gradient flow of a multi-well potential with bending energy |
| title | Spectral approximation of the H-1 gradient flow of a multi-well potential with bending energy |
| title_full | Spectral approximation of the H-1 gradient flow of a multi-well potential with bending energy |
| title_fullStr | Spectral approximation of the H-1 gradient flow of a multi-well potential with bending energy |
| title_full_unstemmed | Spectral approximation of the H-1 gradient flow of a multi-well potential with bending energy |
| title_short | Spectral approximation of the H-1 gradient flow of a multi-well potential with bending energy |
| title_sort | spectral approximation of the h 1 gradient flow of a multi well potential with bending energy |
| work_keys_str_mv | AT sulie spectralapproximationoftheh1gradientflowofamultiwellpotentialwithbendingenergy |