Boundary least squares method with three-dimensional harmonic basis of higher order for solving linear div-curl systems with Dirichlet conditions

Autor:	Marina B. Yuldasheva, Oleg I. Yuldashev
Rok vydání:	2019
Předmět:	010101 applied mathematics Curl (mathematics) Numerical Analysis symbols.namesake Dirichlet conditions Modeling and Simulation Mathematical analysis symbols 010103 numerical & computational mathematics 0101 mathematics 01 natural sciences Mathematics
Zdroj:	Russian Journal of Numerical Analysis and Mathematical Modelling. 34:175-186
ISSN:	1569-3988 0927-6467
DOI:	10.1515/rnam-2019-0015
Popis:	Solving linear divergence-curl system with Dirichlet conditions is reduced to finding an unknown vector function in the space of piecewise-polynomial gradients of harmonic functions. In this approach one can use the boundary least squares method with a harmonic basis of a high order of approximation formulated by the authors previously. The justification of this method is given. The properties of the bilinear form and approximating properties of the basis are investigated. Convergence of approximate solutions is proved. A numerical example with estimates of experimental orders of convergence in $\begin{array}{} {\bf V}_h^p \end{array}$-norm for different parameters h, p (p ⩽ 10) is presented. The method does not require specification of penalty weight function.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::9db41cf6c9f5299f5bab126e94201838 https://doi.org/10.1515/rnam-2019-0015 Zobrazit plný text záznamu