# AdaptiveNonlinearVariationalSolver¶

class dolfin.cpp.fem.AdaptiveNonlinearVariationalSolver(*args)

A class for goal-oriented adaptive solution of nonlinear variational problems.

For a nonlinear variational problem of the form: find u in V satisfying

F(u; v) = 0 for all v in $$\hat V$$

and a corresponding conforming discrete problem: find u_h in V_h satisfying (at least approximately)

F(u_h; v) = 0 for all v in $$\hat V_h$$

and a given goal functional M and tolerance tol, the aim is to find a V_H and a u_H in V_H satisfying the discrete problem such that

|M(u) - M(u_H)| < tol

This strategy is based on dual-weighted residual error estimators designed and automatically generated for the primal problem and subsequent h-adaptivity.

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