Space-time finite element analysis of the advection-diffusion equation using Galerkin/least-square stabilization
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915030181609472 |
|---|---|
| author | Khara, Biswajit Saurabh, Kumar Dyja, Robert Sharma, Anupam Ganapathysubramanian, Baskar |
| author_facet | Khara, Biswajit Saurabh, Kumar Dyja, Robert Sharma, Anupam Ganapathysubramanian, Baskar |
| contents | We present a full space-time numerical solution of the advection-diffusion equation using a continuous Galerkin finite element method on conforming meshes. The Galerkin/least-square method is employed to ensure stability of the discrete variational problem. In the full space-time formulation, time is considered another dimension, and the time derivative is interpreted as an additional advection term of the field variable. We derive a priori error estimates and illustrate spatio-temporal convergence with several numerical examples. We also derive a posteriori error estimates, which coupled with adaptive space-time mesh refinement provide efficient and accurate solutions. The accuracy of the space-time solutions is illustrated against analytical solutions as well as against numerical solutions using a conventional time-marching algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_00822 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Space-time finite element analysis of the advection-diffusion equation using Galerkin/least-square stabilization Khara, Biswajit Saurabh, Kumar Dyja, Robert Sharma, Anupam Ganapathysubramanian, Baskar Numerical Analysis Analysis of PDEs We present a full space-time numerical solution of the advection-diffusion equation using a continuous Galerkin finite element method on conforming meshes. The Galerkin/least-square method is employed to ensure stability of the discrete variational problem. In the full space-time formulation, time is considered another dimension, and the time derivative is interpreted as an additional advection term of the field variable. We derive a priori error estimates and illustrate spatio-temporal convergence with several numerical examples. We also derive a posteriori error estimates, which coupled with adaptive space-time mesh refinement provide efficient and accurate solutions. The accuracy of the space-time solutions is illustrated against analytical solutions as well as against numerical solutions using a conventional time-marching algorithm. |
| title | Space-time finite element analysis of the advection-diffusion equation using Galerkin/least-square stabilization |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2307.00822 |