A conservation-prioritized approach simultaneously enhancing mass and momentum conservation of least-squares method for Stokes/Navier-Stokes problems

In solving the system of Stokes and Navier-Stokes equations, lack of mass conservation has been viewed as the critical drawback of the finite element methods based on the least-squares (LS) principle. Although many modifications have been proposed, there is a need for a global approach that improves both mass conservation and momentum conservation. The key to such a global method is to control local conservation, which is weaker than to control the residual everywhere. Accordingly, a new method named conservation-prioritized Moment Least-Squares (CMLS) is developed. The CMLS method emerges from the moment conditions. Among these moment conditions, the zero-order moment, which exactly expresses the local conservation condition on the element, is prioritized over the others; thereby, good local conservation can be achieved. The advantages of the CMLS method over the LS method are demonstrated by conservation errors, convergence studies, and numerical accuracy in nonlinear Navier-Stokes tests. Besides, the CMLS method retains the merits of the LS method: it has a symmetric positive-definite global matrix and the same interpolation for both velocity and pressure.(c) 2022 Elsevier B.V. All rights reserved.