A posteriori error estimators for hierarchical B-spline discretizations
| Autor: | Eduardo M. Garau, Annalisa Buffa |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
Matemáticas Applied Mathematics B-spline Estimator Matemática Aplicada 010103 numerical & computational mathematics Numerical Analysis (math.NA) hierarchical splines Discretization error 01 natural sciences adaptivity Mathematics::Numerical Analysis Hierarchical splines 010101 applied mathematics Adaptivity Modeling and Simulation FOS: Mathematics A priori and a posteriori Applied mathematics A posteriori error estimators Mathematics - Numerical Analysis 0101 mathematics CIENCIAS NATURALES Y EXACTAS Mathematics |
| Zdroj: | Mathematical Models and Methods in Applied Sciences Mathematical models and methods in applied sciences 28 (2018): 1453–1480. doi:10.1142/S0218202518500392 info:cnr-pdr/source/autori:A. Buffa and E.M. Garau/titolo:A posteriori error estimators for hierarchical B-spline discretizations/doi:10.1142%2FS0218202518500392/rivista:Mathematical models and methods in applied sciences/anno:2018/pagina_da:1453/pagina_a:1480/intervallo_pagine:1453–1480/volume:28 |
| DOI: | 10.48550/arxiv.1611.07816 |
| Popis: | In this paper we develop function-based a posteriori error estimators for the solution of linear second order elliptic problems considering hierarchical spline spaces for the Galerkin discretization. We obtain a global upper bound for the energy error over arbitrary hierarchical mesh configurations which simplifies the implementation of adaptive refinement strategies. The theory hinges on some weighted Poincaré type inequalities where the B-spline basis functions are the weights appearing in the norms. Such inequalities are derived following the lines in (Veeser and Verfürth, 2009), where the case of standard finite elements is considered. Additionally, we present numerical experiments that show the efficiency of the error estimators independently of the degree of the splines used for the discretization, together with an adaptive algorithm guided by these local estimators that yields optimal meshes and rates of convergence, exhibiting an excellent performance. Fil: Buffa, Annalisa. École Polytechnique Fédérale de Lausanne; Suiza. Consiglio Nazionale Delle Ricerche. Instituto Dimatemática Applicata E Tecnologie Informatiche; Italia Fil: Garau, Eduardo Mario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina. Universidad Nacional del Litoral; Argentina |
| Databáze: | OpenAIRE |
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