Let f be an analytic function on a simply-connected compact continuum E of the complex z-
plane. This might be an interval of the real line, where f might be real analytic. How can we …

It is well‐known that when the geometry and/or coefficients allow stable trapped rays, the
outgoing solution operator of the Helmholtz equation grows exponentially through a …

We consider numerical approximations of ill-posed elliptic problems with conditional
stability. The notion of optimal error estimates is defined including both convergence with …

We consider approximating the solution of the Helmholtz exterior Dirichlet problem for a
nontrap** obstacle, with boundary data coming from plane-wave incidence, by the …

The numerical approximation of an inverse problem subject to the convection–diffusion
equation when diffusion dominates is studied. We derive Carleman estimates that are of a …

We consider primal-dual mixed finite element methods for the solution of the elliptic Cauchy
problem, or other related data assimilation problems. The method has a local conservation …

We are interested in solving the unique continuation problem for the heat equation, ie, we
want to reconstruct the solution of the heat equation in a target space-time subdomain given …

In this article, we discuss quantitative Runge approximation properties for the acoustic
Helmholtz equation and prove stability improvement results in the high frequency limit for an …

We design a primal-dual stabilized finite element method for the numerical approximation of
a data assimilation problem subject to the acoustic wave equation. For the forward problem …

We design and analyze an arbitrary-order hybridized discontinuous Galerkin method to
approximate the unique continuation problem subject to the Helmholtz equation. The …