Discrete weak duality of hybrid high-order methods for convex minimization problems
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918435925000192 |
|---|---|
| author | Tran, Ngoc Tien |
| author_facet | Tran, Ngoc Tien |
| contents | This paper derives a discrete dual problem for a prototypical hybrid high-order method for convex minimization problems. The discrete primal and dual problem satisfy a weak convex duality that leads to a priori error estimates with convergence rates under additional smoothness assumptions. This duality holds for general polyhedral meshes and arbitrary polynomial degrees of the discretization. A novel postprocessing is proposed and allows for a~posteriori error estimates on regular triangulations into simplices using primal-dual techniques. This motivates an adaptive mesh-refining algorithm, which performs superiorly compared to uniform mesh refinements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_03223 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Discrete weak duality of hybrid high-order methods for convex minimization problems Tran, Ngoc Tien Numerical Analysis 65N12, 65N30, 65Y20 This paper derives a discrete dual problem for a prototypical hybrid high-order method for convex minimization problems. The discrete primal and dual problem satisfy a weak convex duality that leads to a priori error estimates with convergence rates under additional smoothness assumptions. This duality holds for general polyhedral meshes and arbitrary polynomial degrees of the discretization. A novel postprocessing is proposed and allows for a~posteriori error estimates on regular triangulations into simplices using primal-dual techniques. This motivates an adaptive mesh-refining algorithm, which performs superiorly compared to uniform mesh refinements. |
| title | Discrete weak duality of hybrid high-order methods for convex minimization problems |
| topic | Numerical Analysis 65N12, 65N30, 65Y20 |
| url | https://arxiv.org/abs/2308.03223 |