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A hybrid high-order method for the incompressible Navier-Stokes problem robust for large irrotational body forces. (English) Zbl 1437.65178
Summary: We develop a novel Hybrid High-Order method for the incompressible Navier-Stokes problem robust for large irrotational body forces. The key ingredients of the method are discrete versions of the body force and convective contributions in the momentum equation formulated in terms of a globally divergence-free velocity reconstruction. Two key properties are mimicked at the discrete level, namely the invariance of the velocity with respect to irrotational body forces and the non-dissipativity of the convective term. A full convergence analysis is carried out, showing optimal orders of convergence under a smallness condition involving only the solenoidal part of the body force. The performance of the method is illustrated by a complete panel of numerical tests, including comparisons that highlight the benefits with respect to more standard formulations.
MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
Software:
Eigen; PARDISO
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