An energy-based discontinuous Galerkin method for the wave equation with nonsmooth solutions
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909673336078336 |
|---|---|
| author | Fu, Yangxin Jiang, Yan Wang, Siyang |
| author_facet | Fu, Yangxin Jiang, Yan Wang, Siyang |
| contents | We develop a stable and high-order accurate discontinuous Galerkin method for the second order wave equation, specifically designed to handle nonsmooth solutions. Our approach integrates the energy-based discontinuous Galerkin method with the oscillation-free technique to effectively suppress spurious oscillations near solution discontinuities. Both stability analysis and apriori error estimates are established for common choices of numerical fluxes. We present a series of numerical experiments to confirm the optimal convergence rates for smooth solutions and its robustness in maintaining oscillation-free behavior for nonsmooth solutions in wave equations without or with nonlinear source terms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01736 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An energy-based discontinuous Galerkin method for the wave equation with nonsmooth solutions Fu, Yangxin Jiang, Yan Wang, Siyang Numerical Analysis We develop a stable and high-order accurate discontinuous Galerkin method for the second order wave equation, specifically designed to handle nonsmooth solutions. Our approach integrates the energy-based discontinuous Galerkin method with the oscillation-free technique to effectively suppress spurious oscillations near solution discontinuities. Both stability analysis and apriori error estimates are established for common choices of numerical fluxes. We present a series of numerical experiments to confirm the optimal convergence rates for smooth solutions and its robustness in maintaining oscillation-free behavior for nonsmooth solutions in wave equations without or with nonlinear source terms. |
| title | An energy-based discontinuous Galerkin method for the wave equation with nonsmooth solutions |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2507.01736 |