3 papers
math.NA2024
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…
math.NA2024
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…
math.NA2024
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…