pymor.models.saddle_point

Module Contents

class pymor.models.saddle_point.SaddlePointModel(A, B, f, g=None, C=None, u_product=None, p_product=None, error_estimator=None, visualizer=None, name=None)

Bases: pymor.models.basic.StationaryModel

Generic class for saddle-point models.

Defines a stationary saddle-point model using a 2x2 BlockOperator:

\[\begin{split}\begin{bmatrix} A & B^\ast \\ B & C \end{bmatrix} \begin{bmatrix} u \\ p \end{bmatrix} = \begin{bmatrix} f \\ g \end{bmatrix},\end{split}\]

Here, A maps the u-space into itself, B maps from the u-space to the p-space, and C is optional. If C is provided, it maps the p-space into itself. Typical example: Stokes equation with velocity (u) and pressure (p).

Parameters:

• A – Operator on the u-space with A.source == A.range.

• B – Coupling Operator between the u and p-space with B.source == A.source.

• C – Optional Operator on the p-space. One of: - Operator with C.source == C.range == B.range. - None, which yields a ZeroOperator.

• f – f of the right-hand side. Either: - Linear Operator acting on the u-space with a scalar source space. - VectorArray on the u-space.

• g – g of the right-hand side. Either - Linear Operator acting on the p-space with a scalar source space. - VectorArray on the p-space. - None, then g is set to zero.

• u_product – Inner product Operator acting on the u-space.

• p_product – Inner product Operator acting on the p-space.

• error_estimator – See StationaryModel.

• visualizer – See StationaryModel.

• name – See StationaryModel.