# AdaptiveNonlinearVariationalSolver¶

class dolfin.fem.adaptivesolving.AdaptiveNonlinearVariationalSolver(problem, goal)

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.

Create AdaptiveNonlinearVariationalSolver

Arguments

solve(tol)

Solve such that the estimated error in the functional ‘goal’ is less than the given tolerance ‘tol’.

Arguments

tol (float)

The error tolerance