Browsing by Author "Hajduk H"

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    Locally energy-stable finite element schemes for incompressible flow problems: Design and analysis for equal-order interpolations
    (Elsevier Ltd, 2025-05-30) Hajduk H; Kuzmin D; Lube G; Öffner P
    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.