Mixed finite elements for Bingham flow in a pipe

DOI10.1007/S00211-022-01332-WarXiv2205.11149MaRDI QIDQ6399898

Publication date: 23 May 2022

Abstract: We consider mixed finite element approximations of viscous, plastic Bingham flow in a cylindrical pipe. A novel a priori and a posteriori error analysis is introduced which is based on a discrete mesh dependent norm for the normalized Lagrange multiplier. This allows proving stability for various conforming finite elements. Numerical examples are presented to support the theory and to demonstrate adaptive mesh refinement.

Mathematics Subject Classification ID

Non-Newtonian fluids (76A05) Stability in context of PDEs (35B35) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element methods applied to problems in fluid mechanics (76M10) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

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