scholarly journals Adaptive mesh refinement for time-domain electromagnetics using vector finite elements :a feasibility study.

2005 ◽  
Author(s):  
C David Turner ◽  
Joseph Daniel Kotulski ◽  
Michael Francis Pasik
Keyword(s):  
Finite Elements ◽  
Feasibility Study ◽  
Time Domain ◽  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Vector Finite Elements ◽  
Time Domain Electromagnetics

scholarly journals A Differentiable Mapping of Mesh Cells Based on Finite Elements on Quadrilateral and Hexahedral Meshes

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Daniel Arndt ◽  
Guido Kanschat
Keyword(s):  
Finite Elements ◽  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Differentiable Mapping ◽  
Standard Format ◽  
Efficient Storage ◽  
Hexahedral Meshes

AbstractFinite elements of higher continuity, say conforming in {H^{2}} instead of {H^{1}}, require a mapping from reference cells to mesh cells which is continuously differentiable across cell interfaces. In this article, we propose an algorithm to obtain such mappings given a topologically regular mesh in the standard format of vertex coordinates and a description of the boundary. A variant of the algorithm with orthogonal edges in each vertex is proposed. We introduce necessary modifications in the case of adaptive mesh refinement with nonconforming edges. Furthermore, we discuss efficient storage of the necessary data.

On generalized binomial laws to evaluate finite element accuracy: preliminary probabilistic results for adaptive mesh refinement

2020 ◽  
Vol 28 (2) ◽  
pp. 63-74
Author(s):  
Joël Chaskalovic ◽  
Franck Assous
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Error Estimate ◽  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Random Variable ◽  
Geometrical Interpretation ◽  
Relative Accuracy ◽  
Probabilistic Methods

AbstractThe aim of this paper is to provide new perspectives on the relative finite elements accuracy. Starting from a geometrical interpretation of the error estimate which can be deduced from Bramble–Hilbert lemma, we derive a probability law that evaluates the relative accuracy, considered as a random variable, between two finite elements Pk and Pm, k < m. We extend this probability law to get a cumulated probabilistic law for two main applications. The first one concerns a family of meshes, the second one is dedicated to a sequence of simplexes constituting a given mesh. Both of these applications could be considered as a first step toward application for adaptive mesh refinement with probabilistic methods.

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