Maximum Norm Analysis of a Nonmatching Grids Method for Nonlinear Elliptic Boundary Value Problem −Δu = f(u)
We provide a maximum norm analysis of a finite
element Schwarz alternating method for a nonlinear elliptic boundary
value problem of the form -Δu = f(u), on two overlapping sub
domains with non matching grids. We consider a domain which is
the union of two overlapping sub domains where each sub domain
has its own independently generated grid. The two meshes being
mutually independent on the overlap region, a triangle belonging to
one triangulation does not necessarily belong to the other one. Under
a Lipschitz assumption on the nonlinearity, we establish, on each sub
domain, an optimal L∞ error estimate between the discrete Schwarz
sequence and the exact solution of the boundary value problem.
Error estimates, Finite elements, Nonlinear PDEs, Schwarz method.