A note on least-squares mixed finite elements in relation to standard and mixed finite elements期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

A note on least-squares mixed finite elements in relation to standard and mixed finite elements

Authors:	Brandts, Jan Chen, Yanping Yang, Julie

Affiliation:	¹ Korteweg-de Vries Institute for Mathematics, Faculty of Science, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, Netherlands, ² Institute for Computational and Applied Mathematics, Xiangtan University, Xiangtan 411105, China

Abstract:	^** Email: brandts{at}science.uva.nl The least-squares mixed finite-element method for second-orderelliptic problems yields an approximation u_h $isin$ V_h $sub$ H₀¹( ${Omega}$ ) of thepotential u together with an approximation p_h $isin$ ${Gamma}$ _h $sub$ H(div ; ${Omega}$ )of the vector field p = A ${nabla}$ u. Comparing u_h with the standardfinite-element approximation of u in V_h, and p_h with the mixedfinite-element approximation of p, it turns out that they arehigher-order perturbations of each other. In other words, theyare superclose. Refined a priori bounds and superconvergenceresults can now be proved. Also, the local mass conservationerror is of higher order than could be concluded from the standarda priori analysis.

Keywords:	least-squares mixed finite-element method standard finite-element method mixed finite-element method supercloseness
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