Auxiliary space preconditioning for mixed finite element discretizations of Richards’ equation

Juan Batista, Xiaozhe Hu, Ludmil Tomov Zikatanov

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
JournalComputers and Mathematics with Applications
DOIs
StateAccepted/In press - Jan 1 2019

Fingerprint

Richards Equation
Mixed Finite Elements
Finite Element Discretization
Preconditioning
Mathematical operators
Interpolation
Finite element method
Mixed Methods
Preconditioner
Elliptic Problems
Positive definite
Discretization
Interpolate
Scalar
Operator
Estimate

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

Cite this

@article{f411805bbaa54e8d800b3f3f02f94d3a,
title = "Auxiliary space preconditioning for mixed finite element discretizations of Richards’ equation",
abstract = "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.",
author = "Juan Batista and Xiaozhe Hu and Zikatanov, {Ludmil Tomov}",
year = "2019",
month = "1",
day = "1",
doi = "10.1016/j.camwa.2019.09.011",
language = "English (US)",
journal = "Computers and Mathematics with Applications",
issn = "0898-1221",
publisher = "Elsevier Limited",

}

TY - JOUR

T1 - Auxiliary space preconditioning for mixed finite element discretizations of Richards’ equation

AU - Batista, Juan

AU - Hu, Xiaozhe

AU - Zikatanov, Ludmil Tomov

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85072598181&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85072598181&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2019.09.011

DO - 10.1016/j.camwa.2019.09.011

M3 - Article

AN - SCOPUS:85072598181

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

ER -