A parallel iterative procedure applicable to the approximate solution of second order partial differential equations by mixed finite element methods

SummaryA parallelizable interative procedure based on domain decomposition techniques is defined and analyzed for mixed finite element methods for elliptic equations, with the analysis being presented for the decomposition of the domain into the individual elements associated with the mixed method or into larger subdomains. Applications to time-dependent problems are indicated.

[1]  Jean E. Roberts,et al.  Global estimates for mixed methods for second order elliptic equations , 1985 .

[2]  L. D. Marini,et al.  Two families of mixed finite elements for second order elliptic problems , 1985 .

[3]  M. Fortin,et al.  Mixed finite elements for second order elliptic problems in three variables , 1987 .

[4]  F. Brezzi.  On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers , 1974 .

[5]  M. Fortin,et al.  E cient rectangular mixed fi-nite elements in two and three space variables , 1987 .

[6]  J. Wang,et al.  Analysis of multilevel decomposition iterative methods for mixed finite element methods , 1994 .

[7]  O. C. Holister,et al.  Stress Analysis , 1965 .

[8]  J. Douglas,et al.  Prismatic mixed finite elements for second order elliptic problems , 1989 .

[9]  R. Kellogg,et al.  A regularity result for the Stokes problem in a convex polygon , 1976 .

[10]  Richard E. Ewing,et al.  Incomplete Iteration for Time-Stepping a Galerkin Method for a Quasilinear Parabolic Problem , 1979 .

[11]  B. D. Veubeke.  Displacement and equilibrium models in the finite element method , 1965 .

[12]  D. Arnold,et al.  Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates , 1985 .

[13]  Mary F. Wheeler,et al.  Parallel Domain Decomposition Method for Mixed Finite Elements for Elliptic Partial Differential Equations , 1990 .

[14]  Jim Douglas,et al.  A time-stepping method for Galerkin approximations for nonlinear parabolic equations , 1978 .

[15]  P. Raviart,et al.  A mixed finite element method for 2-nd order elliptic problems , 1977 .

[16]  J. Nédélec.  Mixed finite elements in ℝ3 , 1980 .

[17]  Jr. Jim Douglas.  On Incomplete Iteration for Implicit Parabolic Difference Equations , 1961 .

[18]  D. Arnold.  Mixed finite element methods for elliptic problems , 1990 .

[19]  R. Glowinski,et al.  Third International Symposium on Domain Decomposition Methods for Partial Differential Equations , 1990 .

[20]  B. D. Veubeke.  Stress function approach , 1975 .