This paper utilizes the Picard method and Newton's method to linearize the stationary incompressible Navier–Stokes equations and then uses an LL* approach, which is a least-squares finite element method applied to the dual problem of the corresponding linear system. The LL* approach provides an L2-approximation to a given problem, which is not typically available with conventional finite element methods for nonlinear second-order partial differential equations. We first show that the proposed combination of linearization scheme and LL* approach provides an L2-approximation to the stationary incompressible Navier–Stokes equations. The validity of L2-approximation is proven through the analysis of the weak problem corresponding to the linearized Navier–Stokes equations. Then, the convergence is analyzed, and numerical results are presented.
|Number of pages||16|
|Journal||Numerical Methods for Partial Differential Equations|
|Publication status||Published - 2020 Nov 1|
Bibliographical noteFunding Information:
National Research Foundation of Korea, NRF‐2015R1D1A1A01056909; NRF‐2018R1D1A1B07042973 Funding information
information National Research Foundation of Korea, NRF-2015R1D1A1A01056909; NRF-2018R1D1A1B07042973
© 2020 Wiley Periodicals, Inc.
All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics