Work

A Discrete Trace Theory for Non-Conforming Polytopal Hybrid Discretisation Methods

Year: 2025

Type: article

Abstract: In this work we develop a discrete trace theory that covers non-conforming hybrid discretization methods and holds on polytopal meshes. A notion of discrete trace seminorm is defined, and trace and lifting results with respect to a discrete $$H^1$$ H 1 -seminorm on the hybrid fully discrete space are proven. Finally, we conduct a numerical test in which we compute the proposed discrete operators and investigate their spectrum to verify the theoretical analysis. The development of this theory is motivated by the design and analysis of preconditioners for hybrid methods, e.g., of substructuring domain decomposition type.

Source: Foundations of Computational Mathematics

DOI: 10.1007/s10208-025-09734-6

Authors: Santiago Badia, Jerome Droniou, Jai Tushar

Institutions: Monash University, Centre National de la Recherche Scientifique, Institut Montpelliérain Alexander Grothendieck

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,290

Funders: Australian Government, European Commission, Australian Research Council