An algebraically stabilized method for convection-diffusion-reaction problems with optimal experimental convergence rates on general meshes

[摘要] Algebraically stabilized finite element discretizations of scalar steady-state convection-diffusion-reaction equations often provide accurate approximate solutions satisfying the discrete maximum principle (DMP). However, it was observed that a deterioration of the accuracy and convergence rates may occur for some problems if meshes without local symmetries are used. The paper investigates these phenomena both numerically and analytically and the findings are used to design a new algebraic stabilization called Symmetrized Monotone Upwind-type Algebraically Stabilized (SMUAS) method. It is proved that the SMUAS method is linearity preserving and satisfies the DMP on arbitrary simplicial meshes. Moreover, numerical results indicate that the SMUAS method leads to optimal convergence rates on general simplicial meshes.

[效力级别]  Early Access

[关键词] FINITE-ELEMENT SCHEMES;CORRECTED TRANSPORT ALGORITHMS;DIMINISHING SOLD METHODS;FLUX-CORRECTION;SPURIOUS OSCILLATIONS;MAXIMUM PRINCIPLE;EQUATIONS;DISCRETIZATIONS;LIMITERS