hp-adaptive discontinuous Galerkin finite element methods for first-order hyperbolic problems
We consider the a posteriori error analysis of hp-discontinuous Galerkin finite element approximations to first-order hyperbolic problems. In particular, we discuss the question of error estimation for linear functionals, such as the outflow flux and the local average of the solution. Based on our a...
| Main Authors: | , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
2002
|
| _version_ | 1797074594068168704 |
|---|---|
| author | Houston, P Süli, E |
| author_facet | Houston, P Süli, E |
| author_sort | Houston, P |
| collection | OXFORD |
| description | We consider the a posteriori error analysis of hp-discontinuous Galerkin finite element approximations to first-order hyperbolic problems. In particular, we discuss the question of error estimation for linear functionals, such as the outflow flux and the local average of the solution. Based on our a posteriori error bound we design and implement the corresponding adaptive algorithm to ensure reliable and efficient control of the error in the prescribed functional to within a given tolerance. This involves exploiting both local polynomial-degree variation and local mesh subdivision. The theoretical results are illustrated by a series of numerical experiments. |
| first_indexed | 2024-03-06T23:38:28Z |
| format | Journal article |
| id | oxford-uuid:6e78c5ed-658e-45c1-82c1-26ed7ef289ad |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T23:38:28Z |
| publishDate | 2002 |
| record_format | dspace |
| spelling | oxford-uuid:6e78c5ed-658e-45c1-82c1-26ed7ef289ad2022-03-26T19:24:40Zhp-adaptive discontinuous Galerkin finite element methods for first-order hyperbolic problemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:6e78c5ed-658e-45c1-82c1-26ed7ef289adEnglishSymplectic Elements at Oxford2002Houston, PSüli, EWe consider the a posteriori error analysis of hp-discontinuous Galerkin finite element approximations to first-order hyperbolic problems. In particular, we discuss the question of error estimation for linear functionals, such as the outflow flux and the local average of the solution. Based on our a posteriori error bound we design and implement the corresponding adaptive algorithm to ensure reliable and efficient control of the error in the prescribed functional to within a given tolerance. This involves exploiting both local polynomial-degree variation and local mesh subdivision. The theoretical results are illustrated by a series of numerical experiments. |
| spellingShingle | Houston, P Süli, E hp-adaptive discontinuous Galerkin finite element methods for first-order hyperbolic problems |
| title | hp-adaptive discontinuous Galerkin finite element methods for first-order hyperbolic problems |
| title_full | hp-adaptive discontinuous Galerkin finite element methods for first-order hyperbolic problems |
| title_fullStr | hp-adaptive discontinuous Galerkin finite element methods for first-order hyperbolic problems |
| title_full_unstemmed | hp-adaptive discontinuous Galerkin finite element methods for first-order hyperbolic problems |
| title_short | hp-adaptive discontinuous Galerkin finite element methods for first-order hyperbolic problems |
| title_sort | hp adaptive discontinuous galerkin finite element methods for first order hyperbolic problems |
| work_keys_str_mv | AT houstonp hpadaptivediscontinuousgalerkinfiniteelementmethodsforfirstorderhyperbolicproblems AT sulie hpadaptivediscontinuousgalerkinfiniteelementmethodsforfirstorderhyperbolicproblems |