Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Primal-Dual Weak Galerkin Finite Element Methods for Elliptic Cauchy
  Problems   The authors propose and analyze a well-posed numerical scheme for a type of
ill-posed elliptic Cauchy problem by using a constrained minimization approach
combined with the weak Galerkin finite element method. The resulting
Euler-Lagrange formulation yields a system of equations involving the original
equation for the primal variable and its adjoint for the dual variable, and is
thus an example of the primal-dual weak Galerkin finite element method. This
new primal-dual weak Galerkin algorithm is consistent in the sense that the
system is symmetric, well-posed, and is satisfied by the exact solution. A
certain stability and error estimates were derived in discrete Sobolev norms,
including one in a weak $L^2$ topology. Some numerical results are reported to
illustrate and validate the theory developed in the paper.

11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int