Operators approximating partial derivatives at vertices of triangulations by averaging

Title:

Operators approximating partial derivatives at vertices of triangulations by averaging

Creator:

Dalík, Josef

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:3c68413a-28ef-47f9-b185-d5c455441994
uuid:3c68413a-28ef-47f9-b185-d5c455441994
doi:10.21136/MB.2010.140827

Subject:

partial derivative, high-order approximation, and recovery operator

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Let Th be a triangulation of a bounded polygonal domain Ω ⊂ R2 , Lh the space of the functions from C(Ω) linear on the triangles from Th and Πh the interpolation operator from C(Ω) to Lh. For a unit vector z and an inner vertex a of Th, we describe the set of vectors of coefficients such that the related linear combinations of the constant derivatives ∂Πh(u)/∂z on the triangles surrounding a are equal to ∂u/∂z(a) for all polynomials u of the total degree less than or equal to two. Then we prove that, generally, the values of the so-called recovery operators approximating the gradient ∇u(a) cannot be expressed as linear combinations of the constant gradients ∇Πh(u) on the triangles surrounding a.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

363-372

Source:

Mathematica bohemica | 2010 Volume:135 | Number:4

Harvested from:

CDK

Metadata only:

false