In previous work, the first-order system LL∗ (FOSLL∗) method was developed for linear partial differential equations. This approach seeks to minimize the residual of the equations in a dual norm induced by the differential operator, yielding approximations accurate in L2(Ω) rather than H1(Ω) or H(Div). In this paper, the general framework of FOSLL∗ is extended to a wide range of nonlinear problems. Four approaches to propagating an inexact Newton iteration based on a FOSLL∗ approximation are presented, and theory for robust convergence in L2(Ω) is established. Numerical results are presented for two formulations of the steady incompressible Navier-Stokes equations and for a diffusion equation with reduced regularity due to a discontinuous diffusion coefficient.
All Science Journal Classification (ASJC) codes
- Computational Mathematics
- Applied Mathematics