2016/11/14 by Javier de Frutos, de Frutos, Javier, Bosco Garcı́a-Archilla +3
Engineering · Mathematics · #65M12 #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1611.04510
openalex publication_date 2016/11/14 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
A modified Chorin-Teman (Euler non-incremental) projection method and a\nmodified Euler incremental projection method for non inf-sup stable mixed\nfinite elements are analyzed. The analysis of the classical Euler\nnon-incremental and Euler incremental methods are obtained as a particular\ncase. We first prove that the modified Euler non-incremental scheme has an\ninherent stabilization that allows the use of non inf-sup stable mixed finite\nelements without any kind of extra added stabilization. We show that it is also\ntrue in the case of the classical Chorin-Temam method. For the second scheme,\nwe study a stabilization that allows the use of equal-order pairs of finite\nelements. The relation of the methods with the so called pressure stabilized\nPetrov Galerkin method (PSPG) is established. The influence of the chosen\ninitial approximations in the computed approximations to the pressure is\nanalyzed. Numerical tests confirm the theoretical results.\n