L2-Error Estimates of the Extrapolated Crank-Nicolson Discontinuous Galerkin Approximations for Nonlinear Sobolev Equations
We analyze discontinuous Galerkin methods with penalty terms, namely, symmetric interior penalty Galerkin methods, to solve nonlinear Sobolev equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropri...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2010-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://dx.doi.org/10.1155/2010/895187 |
| _version_ | 1818521252253401088 |
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| author | Hyun Young Lee Mi Ray Ohm Jun Yong Shin |
| author_facet | Hyun Young Lee Mi Ray Ohm Jun Yong Shin |
| author_sort | Hyun Young Lee |
| collection | DOAJ |
| description | We analyze discontinuous Galerkin methods with penalty terms, namely, symmetric interior penalty Galerkin methods, to solve nonlinear Sobolev equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection, which leads to optimal ℓ∞(L2) error estimates of discontinuous Galerkin approximations in both spatial direction and temporal direction. |
| first_indexed | 2024-12-11T01:48:34Z |
| format | Article |
| id | doaj.art-2fcdaba501d449ffa75751c4bdba9e6d |
| institution | Directory Open Access Journal |
| issn | 1025-5834 1029-242X |
| language | English |
| last_indexed | 2024-12-11T01:48:34Z |
| publishDate | 2010-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-2fcdaba501d449ffa75751c4bdba9e6d2022-12-22T01:24:49ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2010-01-01201010.1155/2010/895187L2-Error Estimates of the Extrapolated Crank-Nicolson Discontinuous Galerkin Approximations for Nonlinear Sobolev EquationsHyun Young LeeMi Ray OhmJun Yong ShinWe analyze discontinuous Galerkin methods with penalty terms, namely, symmetric interior penalty Galerkin methods, to solve nonlinear Sobolev equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection, which leads to optimal ℓ∞(L2) error estimates of discontinuous Galerkin approximations in both spatial direction and temporal direction.http://dx.doi.org/10.1155/2010/895187 |
| spellingShingle | Hyun Young Lee Mi Ray Ohm Jun Yong Shin L2-Error Estimates of the Extrapolated Crank-Nicolson Discontinuous Galerkin Approximations for Nonlinear Sobolev Equations Journal of Inequalities and Applications |
| title | L2-Error Estimates of the Extrapolated Crank-Nicolson Discontinuous Galerkin Approximations for Nonlinear Sobolev Equations |
| title_full | L2-Error Estimates of the Extrapolated Crank-Nicolson Discontinuous Galerkin Approximations for Nonlinear Sobolev Equations |
| title_fullStr | L2-Error Estimates of the Extrapolated Crank-Nicolson Discontinuous Galerkin Approximations for Nonlinear Sobolev Equations |
| title_full_unstemmed | L2-Error Estimates of the Extrapolated Crank-Nicolson Discontinuous Galerkin Approximations for Nonlinear Sobolev Equations |
| title_short | L2-Error Estimates of the Extrapolated Crank-Nicolson Discontinuous Galerkin Approximations for Nonlinear Sobolev Equations |
| title_sort | l2 error estimates of the extrapolated crank nicolson discontinuous galerkin approximations for nonlinear sobolev equations |
| url | http://dx.doi.org/10.1155/2010/895187 |
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