A note on the W1,p‐stability of piecewise linear interpolation

Dickopf, Thomas

doi:10.1002/pamm.201210364

Cited by 1 publication

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“…We desribe the diverse transfer concepts only briefly. Their theoretical properties are elaborated in [8] and [5,6]; in particular, one usually studies stability and approximation properties for (shape regular or quasi-uniform) families of meshes as well as locality and projection properties. Also the algorithmic structure and the implementation are covered in [8].…”

Section: Overview Of the Studied Transfer Operatorsmentioning

confidence: 99%

The influence of boundary approximation on transfer operators between non‐nested meshes

Dickopf

Krause

2013

Proc Appl Math and Mech

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Finite element methods with non-matching meshes can offer increased flexibility in many applications. Although the specific reasons for the use of non-matching meshes are apparently diverse, the common difficulty in all these numerical methods is the transfer of finite element approximation associated with one mesh to finite element approximation associated with another mesh. This paper complements previous quantitative studies of transfer operators between finite element spaces associated with unrelated meshes (T. Dickopf, R. Krause, Evaluating local approximations of the L 2 -orthogonal projection between non-nested finite element spaces, Tech. Rep. 2012-01, Institute of Computational Science, Università della Svizzera italiana, 2012). We study the important use case in which functions are mapped between a regular background mesh and an unstructured mesh of a complex geometry. Here, the former does not approximate the latter.

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Section: Overview Of the Studied Transfer Operatorsmentioning

confidence: 99%