Work

Locally energy-stable finite element schemes for incompressible flow problems: Design and analysis for equal-order interpolations

Year: 2025

Type: article

Abstract: We show that finite element discretizations of incompressible flow problems can be designed to ensure preservation/dissipation of kinetic energy not only globally but also locally. In the context of equal-order (piecewise-linear) interpolations, we prove the validity of a semi-discrete energy inequality for a quadrature-based approximation to the nonlinear convective term, which we combine with the Becker–Hansbo pressure stabilization. An analogy with entropy-stable algebraic flux correction schemes for the compressible Euler equations and the shallow water equations yields a weak ‘bounded variation’ estimate from which we deduce the semi-discrete Lax–Wendroff consistency and convergence towards dissipative weak solutions. The results of our numerical experiments for standard test problems confirm that the method under investigation is non-oscillatory and exhibits optimal convergence behavior.

Source: Computers & Fluids

DOI: 10.1016/j.compfluid.2025.106622

Authors: Hennes Hajduk, Dmitri Kuzmin, Gert Lube, Philipp Öffner

Institutions: University of Oslo, TU Dortmund University, University of Göttingen, Clausthal University of Technology

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,700

Funders: Deutsche Forschungsgemeinschaft, Norges Forskningsråd, Technische Universität Dortmund