Formulation of alternating-direction iterative methods for mixed methods in three space. (English) Zbl 0609.65071

Numerical approximation of partial differential equations, Sel. Pap. Int. Symp. Numer. Anal., Madrid/Spain 1985, North-Holland Math. Stud. 133, 21-30 (1987).
[For the entire collection see Zbl 0599.00010.]
Two alternating-direction iterative methods are formulated to treat the linear algebraic equations that arise from the mixed finite element approximation of a second order elliptic boundary value problem in three space variables. One is based on the Uzawa technique for iterating to a solution of a saddle point problem and the other on the Arrow-Hurwitz method for saddle point problems. The Uzawa version is analyzed in a special case. Some preliminary computational results are presented.


65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
35J25 Boundary value problems for second-order elliptic equations


Zbl 0599.00010