6 papers · 1 filter
Latent Inversion of Material Coefficients from Boundary Data via Finite Tests and Neural Surrogates
Erik Burman, Mats G. Larson, Karl Larsson +1
We reconstruct a spatially varying material coefficient in a scalar elliptic equation from finitely many boundary excitations, each producing a full Dirichlet trace. To mitigate th…
Normal Equations and Discrete Energy Structures for High-Order Streamline Diffusion
Erik Burman, Peter Hansbo, Mats G. Larson
We analyse fully discrete Streamline Diffusion finite element methods, also known as SUPG methods, for time-dependent first-order systems with skew-symmetric spatial operators. To…
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…
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…
Hybridized Augmented Lagrangian Methods for Contact Problems
Erik Burman, Peter Hansbo, Mats G. Larson
This paper addresses the problem of friction-free contact between two elastic bodies. We develop an augmented Lagrangian method that provides computational convenience by reformula…
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…