×

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.

MSC:

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

Citations:

Zbl 0599.00010