Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A finite element method for fully nonlinear elliptic problems   We present a continuous finite element method for some examples of fully
nonlinear elliptic equation. A key tool is the discretisation proposed in
Lakkis & Pryer (2011, SISC) allowing us to work directly on the strong form of
a linear PDE. An added benefit to making use of this discretisation method is
that a recovered (finite element) Hessian is a biproduct of the solution
process. We build on the linear basis and ultimately construct two different
methodologies for the solution of second order fully nonlinear PDEs. Benchmark
numerical results illustrate the convergence properties of the scheme for some
test problems including the Monge-Amp\`ere equation and Pucci's equation.

25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn