*(English)*Zbl 1024.65044

The author generates the Babuška-Brezzi theory to a class of nonlinear variational problems with constraints. He considers the operator equations with a dual-dual type structure,

where $(\mathcal{F},\mathcal{G})$ is given, the operator $A$ itself presents also the dual structure $A=\left(\begin{array}{cc}{A}_{1}& {B}_{1}^{*}\\ {B}_{1}& 0\end{array}\right)$, $B$ and ${B}_{1}$ are linear and bounded, and ${A}_{1}$ is nonlinear. He provides sufficient conditions for the existence and uniqueness of solutions to the continuous and Galerkin formulations and derives a Strang-type estimate for the associated error. Moreover, he presents an application to the coupling of mixed finite elements and boundary elements for a nonlinear transmission problem in potential theory.

##### MSC:

65J15 | Equations with nonlinear operators (numerical methods) |

47J25 | Iterative procedures (nonlinear operator equations) |

35J65 | Nonlinear boundary value problems for linear elliptic equations |

65N15 | Error bounds (BVP of PDE) |

65N50 | Mesh generation and refinement (BVP of PDE) |

65N38 | Boundary element methods (BVP of PDE) |