Local  a posteriori  error estimates and adaptive control of pollution effects | Zendy

Liao Xiaohai | Zendy; Nochetto Ricardo H. | Zendy

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Local a posteriori error estimates and adaptive control of pollution effects

Author(s) -

Liao Xiaohai,

Nochetto Ricardo H.

Publication year - 2003

Publication title -

numerical methods for partial differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.901

H-Index - 61

eISSN - 1098-2426

pISSN - 0749-159X

DOI - 10.1002/num.10053

Subject(s) - estimator , a priori and a posteriori , mathematics , upper and lower bounds , basis (linear algebra) , polygon mesh , partial derivative , partial differential equation , error detection and correction , mathematical optimization , algorithm , statistics , mathematical analysis , geometry , philosophy , epistemology

Local a posteriori error estimators are derived for linear elliptic problems over general polygonal domains in 2d. The estimators lead to a sharp upper bound for the energy error in a local region of interest. This upper bound consists of H 1 ‐type local error indicators in a slightly larger subdomain, plus weighted L 2 ‐type local error indicators outside this subdomain, which account for the pollution effects. This constitutes the basis of a local adaptive refinement procedure. Numerical experiments show a superior performance than the standard global procedure as well as the generation of locally quasi‐optimal meshes. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 421–442, 2003

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