A least-squares weak Galerkin FEM is developed for the Cauchy problem in the Helmholtz equation, with proofs of uniqueness and optimal error estimates in a discrete energy norm.
Nanfuka et al., Solving the Cauchy problem for the Helmholtz equation using cubic smoothing splines, Inverse Problems in Science and Engineering
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A Least-Squares Weak Galerkin Finite Element Scheme for Cauchy Problems in Helmholtz
A least-squares weak Galerkin FEM is developed for the Cauchy problem in the Helmholtz equation, with proofs of uniqueness and optimal error estimates in a discrete energy norm.