Least-squares finite element methods

By Pavel B. Bochev, Max D. Gunzburger. 2007

59 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/4b60bb3ca19bebdf2a7bf1e0696153dd57fe560e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Hadi Meidani
2. Rini Jasmine Gladstone
3. Mohammad Amin Nabian
4. R. Matousek
5. Jakub Kudela

In Electrical and Electronic Engineering

1. Hadi Meidani
2. Rini Jasmine Gladstone
3. Mohammad Amin Nabian

In Mechanics of Materials

1. Hadi Meidani
2. Rini Jasmine Gladstone
3. Mohammad Amin Nabian

Citations in the corpus

• A Deep Neural Network Surrogate for High-Dimensional Random Partial Differential Equations (2018, methodology): “In the first approach, similar in spirit to the Least-Square Finite Element Methods (LSFEM) [26], we minimize the squared residual over the entire computational domain, with the random PDE solution represented in form of a feed-forward fully-connected deep residual network.”
• Efficient training of physics‐informed neural networks via importance sampling (2021, methodology): “With soft assignment of constraints, we solve the following unconstrained optimization problem in which λ 1 and λ 2 are weight parameters, analogous to collocation finite element method in which weights are used to adjust the relative importance of each residual term [43].”