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MATHEMATICA BOHEMICA, Vol. 127, No. 2, pp. 153-161 (2002)
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# A stable and optimal complexity solution method for mixed finite element discretizations

## Jan Brandts, Rob Stevenson

* Jan H. Brandts*, Utrecht University, Mathematical Institute, P. O. Box 80.010, 3508 TA, Utrecht, Netherlands, e-mail: ` brandts@math.nu.nl`; * Rob Stevenson*, Utrecht University, Mathematical Institute, P. O. Box 80.010, 3508 TA, Utrecht, Netherlands, e-mail: ` stevenso@math.uu.nl`

**Abstract:**
We outline a solution method for mixed finite element discretizations based on dissecting the problem into three separate steps. The first handles the inhomogeneous constraint, the second solves the flux variable from the homogeneous problem, whereas the third step, adjoint to the first, finally gives the Lagrangian multiplier. We concentrate on aspects involved in the first and third step mainly, and advertise a multi-level method that allows for a stable computation of the intermediate and final quantities in optimal computational complexity.

**Keywords:** mixed finite elements, multi-level solver

**Classification (MSC2000):** 65N30, 65N55, 65F05

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