Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improving Newton's method performance by parametrization: the case of
  Richards equation   The nonlinear systems obtained by discretizing degenerate parabolic equations
may be hard to solve, especially with Newton's method. In this paper, we apply
to Richards equation a strategy that consists in defining a new primary unknown
for the continuous equation in order to stabilize Newton's method by
parametrizing the graph linking the pressure and the saturation. The resulting
form of Richards equation is then discretized thanks to a monotone Finite
Volume scheme. We prove the well-posedness of the numerical scheme. Then we
show under appropriate non-degeneracy conditions on the parametrization that
Newton\^as method converges locally and quadratically. Finally, we provide
numerical evidences of the efficiency of our approach.

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The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an