Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Carleman-based numerical method for quasilinear elliptic equations
  with over-determined boundary data and applications   We propose a new iterative scheme to compute the numerical solution to an
over-determined boundary value problem for a general quasilinear elliptic PDE.
The main idea is to repeatedly solve its linearization by using the
quasi-reversibility method with a suitable Carleman weight function. The
presence of the Carleman weight function allows us to employ a Carleman
estimate to prove the convergence of the sequence generated by the iterative
scheme above to the desired solution. The convergence of the iteration is fast
at an exponential rate without the need of an initial good guess. We apply this
method to compute solutions to some general quasilinear elliptic equations and
a large class of first-order Hamilton-Jacobi equations. Numerical results are
presented.

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The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
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The categories of this paper are: eess
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th