A finite volume discretization of the mixed form of Richards' equation leads to a nonlinear numerical model which yields exact local and global mass conservation. The resulting nonlinear system requires sophisticated numerical strategies, especially in a variable saturated flow regime. In this paper a nested, Newton-type algorithm for the discretized Richards' equation is proposed and analyzed. With a judicious choice of the initial guess, the quadratic convergence rate is obtained for any time step size and for all flow regimes.

MSC codes

  1. 65M08
  2. 65M12
  3. 76M12
  4. 76S05


  1. Richards' equation
  2. variably saturated flow
  3. finite volume
  4. mildly nonlinear systems
  5. Jordan decomposition
  6. nested iterations

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Information & Authors


Published In

cover image SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Pages: 2255 - 2273
ISSN (online): 1095-7197


Submitted: 19 February 2010
Accepted: 9 June 2010
Published online: 29 July 2010

MSC codes

  1. 65M08
  2. 65M12
  3. 76M12
  4. 76S05


  1. Richards' equation
  2. variably saturated flow
  3. finite volume
  4. mildly nonlinear systems
  5. Jordan decomposition
  6. nested iterations



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