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Gauss Newton Method for Solving Variational Problems of PDEs with Neural Network Discretizaitons
The numerical solution of differential equations using machine learning-based approaches has gained significant popularity. Neural network-based discretization has emerged as a powerful tool for solving differ...
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Robust Approximation of Generalized Biot-Brinkman Problems
The generalized Biot-Brinkman equations describe the displacement, pressures and fluxes in an elastic medium permeated by multiple viscous fluid networks and can be used to study complex poromechanical interac...
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New discontinuous Galerkin algorithms and analysis for linear elasticity with symmetric stress tensor
This paper presents a new and unified approach to the derivation and analysis of many existing, as well as new discontinuous Galerkin methods for linear elasticity problems. The analysis is based on a unified ...
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A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations
We consider multigrid methods for discontinuous Galerkin \(H({\text {div}},\Omega )\) ...