106 citations · 530 across the 81 of their papers we have counts for
97 papers
An Unfitted Hybrid High-Order Method for the Elastodynamics Problem with Imperfect Interface
Peiqi Huang, Erik Burman
We design and analyse an unfitted hybrid high-order (HHO) method for the elastic wave equation in a medium made of two components separated by an imperfect interface of linear slip…
A Hybrid High-Order Method for the Elasticity Problem with Linear Slip Interface
Erik Burman, Peiqi Huang
We design and analyse a hybrid high-order (HHO) method for the linear elasticity problem with a linear slip interface, i.e.\ with interface conditions of spring type, in which the…
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…