5 papers
Error Estimates for Nitsche's Method on Approximate Domains
Mats G. Larson, Karl Larsson, Shantiram Mahata
We derive a priori error estimates for Nitsche's method applied to elliptic problems on approximate domains. Such approximations arise, for example, in unfitted finite element meth…
Solving Inverse Parametrized Problems via Finite Elements and Extreme Learning Networks
Erik Burman, Mats G. Larson, Karl Larsson +1
We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. Th…
Cut Finite Element Methods for Convection-Diffusion in Mixed-Dimensional Domains
Erik Burman, Peter Hansbo, Mats G. Larson +2
We develop a cut finite element method (CutFEM) for convection-diffusion problems posed on mixed-dimensional domains, i.e., unions of manifolds of different dimensions arranged in…
Robust Trimmed Multipatch IGA with Singular Maps
Tobias Jonsson, Mats G. Larson, Karl Larsson
We consider elliptic problems in multipatch isogeometric analysis (IGA) where the patch parameterizations may be singular. Specifically, we address cases where certain dimensions o…
Stabilizing and Solving Unique Continuation Problems by Parameterizing Data and Learning Finite Element Solution Operators
Erik Burman, Mats G. Larson, Karl Larsson +1
We consider an inverse problem involving the reconstruction of the solution to a nonlinear partial differential equation (PDE) with unknown boundary conditions. Instead of direct b…