| Title: |
Inf-sup stable space–time Local Discontinuous Galerkin method for the heat equation |
| Authors: |
Gómez S.; Perinati C.; Stocker P. |
| Contributors: |
Gómez, S; Perinati, C; Stocker, P |
| Publisher Information: |
Springer; US |
| Publication Year: |
2026 |
| Collection: |
Università degli Studi di Milano-Bicocca: BOA (Bicocca Open Archive) |
| Subject Terms: |
Inf-sup stability; Local Discontinuous Galerkin method; Parabolic problem; Prismatic space–time meshe; Space–time finite element method |
| Description: |
We propose and analyze a space-time Local Discontinuous Galerkin method for the approximation of the solution to parabolic problems. The method allows for very general discrete spaces and prismatic space-time meshes. Existence and uniqueness of a discrete solution are shown by means of an inf-sup condition, whose proof does not rely on polynomial inverse estimates. Moreover, for piecewise polynomial spaces satisfying an additional mild condition, we show a second inf-sup condition that provides additional control over the time derivative of the discrete solution. We derivehp-a priori error bounds based on these inf-sup conditions, which we use to prove convergence rates for standard, tensor-product, and quasi-Trefftz polynomial spaces. Numerical experiments validate our theoretical results. |
| Document Type: |
article in journal/newspaper |
| File Description: |
STAMPA |
| Language: |
English |
| Relation: |
info:eu-repo/semantics/altIdentifier/pmid/41357096; info:eu-repo/semantics/altIdentifier/wos/WOS:001631359800002; volume:106; issue:1; journal:JOURNAL OF SCIENTIFIC COMPUTING; https://hdl.handle.net/10281/580862 |
| DOI: |
10.1007/s10915-025-03121-7 |
| Availability: |
https://hdl.handle.net/10281/580862; https://doi.org/10.1007/s10915-025-03121-7 |
| Rights: |
info:eu-repo/semantics/openAccess ; license:Creative Commons ; license uri:http://creativecommons.org/licenses/by/4.0/ |
| Accession Number: |
edsbas.9E20DF9F |
| Database: |
BASE |