4 citations · 7 across the 13 of their papers we have counts for
5 papers · 2 filters
Optimal finite element approximation of unique continuation
Erik Burman, Mihai Nechita, Lauri Oksanen
We consider finite element approximations of ill-posed elliptic problems with conditional stability. The notion of {\emph{optimal error estimates}} is defined including both conver…
Unique continuation for an elliptic interface problem using unfitted isoparametric finite elements
Erik Burman, Janosch Preuss
We study unique continuation over an interface using a stabilized unfitted finite element method tailored to the conditional stability of the problem. The interface is approximated…
Best approximation results and essential boundary conditions for novel types of weak adversarial network discretizations for PDEs
Silvia Bertoluzza, Erik Burman, Cuiyu He
In this paper, we provide a theoretical analysis of the recently introduced weakly adversarial networks (WAN) method, used to approximate partial differential equations in high dim…
Finite element approximation of unique continuation of functions with finite dimensional trace
Erik Burman, Lauri Oksanen
We consider a unique continuation problem where the Dirichlet trace of the solution is known to have finite dimension. We prove Lipschitz stability of the unique continuation probl…
A primal dual mixed finite element method for inverse identification of the diffusion coefficient and its relation to the Kohn-Vogelius penalty method
Erik Burman
We revisit the celebrated Kohn-Vogelius penalty method and discuss how to use it for the unique continuation problem where data is given in the bulk of the domain. We then show tha…