Theory of adaptive finite element methods: An introduction
By Ricardo H. Nochetto, Kunibert G. Siebert, Andreas Veeser. 2009
304 citations recorded by the source corpus.
Subfields: Computational Mechanics, Computational Theory and Mathematics, Electrical and Electronic Engineering
View Paper: https://www.semanticscholar.org/paper/bf0784a444404c22d80527e171479642b349f37f
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
- T. Nissen‐Meyer
- Andrew Markham
- Benjamin Moseley
- Hengguang Li
- E. M. Garau
- Juan P. Agnelli
- Herbert Egger
- G. Em Karniadakis
In Computational Theory and Mathematics
- Wei Cai
- Herbert Egger
- G. Em Karniadakis
- Christian Waluga
- Hengguang Li
- Paris Perdikaris
- Dongbin Xiu
- Maizar Raissi
In Electrical and Electronic Engineering
- Hengguang Li
- T. Nissen‐Meyer
- Herbert Egger
- G. Em Karniadakis
- Benjamin Moseley
- Christian Waluga
- Xiaozhe Hu
- Andrew Markham
Citations in the corpus
- The phase field method for geometric moving interfaces and their numerical approximations (2019, unknown): “The first technique gives rise so-called residual-based error bounds [181, 328, 60, 338], and the second one is a duality-based technique, called the Dual Weighted Residual method, which leads to goal-oriented error estimates [30].”
- A Posteriori Error Estimates for the Weak Galerkin Finite Element Methods on Polytopal Meshes (2019, background): “Adaptive finite element methods [20] are widely used in modern computational science and engineering to obtain better accuracy with minimal effort.”
- Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations (2021, background): “For example, many of today’s applications require the study of multi-physics, multi-scale systems, which can be very challenging to incorporate and model accurately, often requiring the use of adaptive schemes and subgrid parameterisations [6, 7].”
- hp analysis of a hybrid DG method for Stokes flow (2013, background): “At the end of this section, let us note that both estimators are assembled from local contributions They are therefore well suited to guide adaptive mesh refinement [62, 51, 47].”
- A posteriori error estimates for elliptic problems with Dirac measure terms in weighted spaces (2014, background): “It is worth mentioning that there are presently no results of optimal complexity for adaptive methods applied to problems involving different ansatz and test spaces (see [26] and references therein).”
- Adaptive finite element method for fractional differential equations using hierarchical matrices (2016, methodology): “In this work, we use the socalled Döflers marking strategy [24] with the detailed algorithm listed below (Algorithm 7).”