Auxiliary space preconditioning for mixed finite element discretizations of Richards’ equation
- Resource Type
- Authors
- Ludmil T. Zikatanov; Xiaozhe Hu; Juan Batista
- Source
- Computers & Mathematics with Applications. 80:405-416
- Subject
- Computational Mathematics
Computational Theory and Mathematics
Discretization
Preconditioner
Modeling and Simulation
Scalar (mathematics)
Applied mathematics
Richards equation
Positive-definite matrix
Numerical tests
Solver
Finite element method
Mathematics
- Language
- ISSN
- 0898-1221
We propose an auxiliary space method for the solution of the indefinite problem arising from mixed method finite element discretizations of scalar elliptic problems. The proposed technique uses conforming elements as an auxiliary space and utilizes special interpolation operators for the transfer of residuals and corrections between the spaces. We show that the corresponding method provides optimal solver for the indefinite problem by only solving symmetric and positive definite auxiliary problems. We apply this preconditioner to the mixed form discretization of Richards’ equation linearized with the L-scheme. We provide numerical tests validating the theoretical estimates.