Mats G. Larson

Learning Nonlinear Finite Element Solution Operators Using Multilayer Perceptrons and Energy Minimization

Abstract. We develop and evaluate a method for learning solution operators to nonlinear problems governed by partial differential equations (PDEs). The approach is based on a finite element discretization and aims at representing the solution operator by a multilayer perceptron t...

Error estimates for Nitsche’s method on approximate domains

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 methods, data-driven simulations, and evolving domain problems, where the computational domain does not...