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FOSLL* FOR NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS
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DOI：10.1137/140974353.png)
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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 L-2(Omega) rather than H-1(Omega) 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 L-2(Omega) 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.
Keyword:
nonlinear partial differential equations
Newton's method
least-squares finite element methods
first-order system LL* method
Navier-Stokes
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