The Time Discontinuous H1-Galerkin Mixed Finite Element Method for Linear Sobolev Equations
We combine the H1-Galerkin mixed finite element method with the time discontinuous Galerkin method to approximate linear Sobolev equations. The advantages of these two methods are fully utilized. The approximate schemes are established to get the approximate solutions by a piecewise polynomial of de...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/618258 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832558590601199616 |
|---|---|
| author | Hong Yu Tongjun Sun Na Li |
| author_facet | Hong Yu Tongjun Sun Na Li |
| author_sort | Hong Yu |
| collection | DOAJ |
| description | We combine the H1-Galerkin mixed finite element method with the time discontinuous Galerkin method to approximate linear Sobolev equations. The advantages of these two methods are fully utilized. The approximate schemes are established to get the approximate solutions by a piecewise polynomial of degree at most q-1 with the time variable. The existence and uniqueness of the solutions are proved, and the optimal H1-norm error estimates are derived. We get high accuracy for both the space and time variables. |
| format | Article |
| id | doaj-art-5c64edd1743e4ed5980193ea342f53df |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-5c64edd1743e4ed5980193ea342f53df2025-02-03T01:31:57ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/618258618258The Time Discontinuous H1-Galerkin Mixed Finite Element Method for Linear Sobolev EquationsHong Yu0Tongjun Sun1Na Li2Basic Subject Department, Shandong Women’s University, Jinan, Shandong 250300, ChinaSchool of Mathematics, Shandong University, Jinan, Shandong 250100, ChinaBasic Subject Department, Shandong Women’s University, Jinan, Shandong 250300, ChinaWe combine the H1-Galerkin mixed finite element method with the time discontinuous Galerkin method to approximate linear Sobolev equations. The advantages of these two methods are fully utilized. The approximate schemes are established to get the approximate solutions by a piecewise polynomial of degree at most q-1 with the time variable. The existence and uniqueness of the solutions are proved, and the optimal H1-norm error estimates are derived. We get high accuracy for both the space and time variables.http://dx.doi.org/10.1155/2015/618258 |
| spellingShingle | Hong Yu Tongjun Sun Na Li The Time Discontinuous H1-Galerkin Mixed Finite Element Method for Linear Sobolev Equations Discrete Dynamics in Nature and Society |
| title | The Time Discontinuous H1-Galerkin Mixed Finite Element Method for Linear Sobolev Equations |
| title_full | The Time Discontinuous H1-Galerkin Mixed Finite Element Method for Linear Sobolev Equations |
| title_fullStr | The Time Discontinuous H1-Galerkin Mixed Finite Element Method for Linear Sobolev Equations |
| title_full_unstemmed | The Time Discontinuous H1-Galerkin Mixed Finite Element Method for Linear Sobolev Equations |
| title_short | The Time Discontinuous H1-Galerkin Mixed Finite Element Method for Linear Sobolev Equations |
| title_sort | time discontinuous h1 galerkin mixed finite element method for linear sobolev equations |
| url | http://dx.doi.org/10.1155/2015/618258 |
| work_keys_str_mv | AT hongyu thetimediscontinuoush1galerkinmixedfiniteelementmethodforlinearsobolevequations AT tongjunsun thetimediscontinuoush1galerkinmixedfiniteelementmethodforlinearsobolevequations AT nali thetimediscontinuoush1galerkinmixedfiniteelementmethodforlinearsobolevequations AT hongyu timediscontinuoush1galerkinmixedfiniteelementmethodforlinearsobolevequations AT tongjunsun timediscontinuoush1galerkinmixedfiniteelementmethodforlinearsobolevequations AT nali timediscontinuoush1galerkinmixedfiniteelementmethodforlinearsobolevequations |