Comparison of the stability of discontinuous Galerkin and finite-difference methods
In this article we present stability analysis of two discrete schemes, which are used to solve a parabolic problem on adaptive nonstationary meshes. The influence of interpolation and projection errors is investigated. It is proved that interpolation error accumulates during computations while proj...
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2002-12-01
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| Series: | Lietuvos Matematikos Rinkinys |
| Online Access: | https://www.zurnalai.vu.lt/LMR/article/view/33038 |
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| _version_ | 1825197264838066176 |
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| author | Raimondas Čiegis Remigijus Čiegis Olga Suboč |
| author_facet | Raimondas Čiegis Remigijus Čiegis Olga Suboč |
| author_sort | Raimondas Čiegis |
| collection | DOAJ |
| description |
In this article we present stability analysis of two discrete schemes, which are used to solve a parabolic problem on adaptive nonstationary meshes. The influence of interpolation and projection errors is investigated. It is proved that interpolation error accumulates during computations while projection error has much better stability properties. Numerical examples illustrate these theoretical results.
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| format | Article |
| id | doaj-art-adb906aa643b4b25a588d7cee4d91fe7 |
| institution | Kabale University |
| issn | 0132-2818 2335-898X |
| language | English |
| publishDate | 2002-12-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Lietuvos Matematikos Rinkinys |
| spelling | doaj-art-adb906aa643b4b25a588d7cee4d91fe72025-02-11T18:13:13ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X2002-12-0142spec.10.15388/LMR.2002.33038Comparison of the stability of discontinuous Galerkin and finite-difference methodsRaimondas Čiegis0Remigijus Čiegis1Olga Suboč2Vilnius Gediminas Technical UniversityVilniaus UniversityVilniaus University In this article we present stability analysis of two discrete schemes, which are used to solve a parabolic problem on adaptive nonstationary meshes. The influence of interpolation and projection errors is investigated. It is proved that interpolation error accumulates during computations while projection error has much better stability properties. Numerical examples illustrate these theoretical results. https://www.zurnalai.vu.lt/LMR/article/view/33038 |
| spellingShingle | Raimondas Čiegis Remigijus Čiegis Olga Suboč Comparison of the stability of discontinuous Galerkin and finite-difference methods Lietuvos Matematikos Rinkinys |
| title | Comparison of the stability of discontinuous Galerkin and finite-difference methods |
| title_full | Comparison of the stability of discontinuous Galerkin and finite-difference methods |
| title_fullStr | Comparison of the stability of discontinuous Galerkin and finite-difference methods |
| title_full_unstemmed | Comparison of the stability of discontinuous Galerkin and finite-difference methods |
| title_short | Comparison of the stability of discontinuous Galerkin and finite-difference methods |
| title_sort | comparison of the stability of discontinuous galerkin and finite difference methods |
| url | https://www.zurnalai.vu.lt/LMR/article/view/33038 |
| work_keys_str_mv | AT raimondasciegis comparisonofthestabilityofdiscontinuousgalerkinandfinitedifferencemethods AT remigijusciegis comparisonofthestabilityofdiscontinuousgalerkinandfinitedifferencemethods AT olgasuboc comparisonofthestabilityofdiscontinuousgalerkinandfinitedifferencemethods |