A high-order local projection stabilization method for natural convection problems
The paper is concerned with the analysis of the local projection stabilization finite element method for natural convection problems governed by the Boussinesq-Navier-Stokes systems. Since the standard finite element method for these systems typically leads to solutions with spurious oscillations at high Rayleigh numbers, the authors focus on the stabilization of the method. They propose a local projection stabilization that is based on the interpolation-stabilized structure rather than on the standard projection-stabilized structure. The authors prove that the proposed scheme is stable and convergent, and they derive optimal error estimates. To illustrate the efficiency and reliability of the method, the numerical experiments are provided for the 2D motion of a fluid in a square cavity with differentially heated side walls at high Rayleigh numbers and the results are compared with benchmark solutions. The method gives sufficiently accurate solutions on relatively coarse grids.
scientific article; zbMATH DE number 6858868
scientific article