CONVERGENCE AND OPTIMALITY OF ADAPTIVE MIXED METHODS FOR POISSON’S EQUATION IN THE FEEC FRAMEWORK
作者机构：Department of MathematicsUniversity of CaliforniaSan DiegoCA 92123USA Department of Mathematics and StatisticsCal Poly PomonaUSA
出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)
年 卷 期：2020年第38卷第5期
页 面：748-767页
核心收录：
学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 070101[理学-基础数学]
基 金：MS was partially supported by NSF Awards 1620366 1262982 and 1217175.YL was partially supported by NSF Award 1620366.AM adn RS were partially supported by NSF Award 1217175
主 题：Finite Element Exterior Calculus Adaptive finite element methods A posteriori error estimates,Convergence Quasi-optimality
摘 要：Finite Element Exterior Calculus (FEEC) was developed by Arnold, Falk, Winther andothers over the last decade to exploit the observation that mixed variational problems canbe posed on a Hilbert complex, and Galerkin-type mixed methods can then be obtained bysolving finite-dimensional subcomplex problems. Chen, Holst, and Xu (Math. Comp. 78(2009) 35–53) established convergence and optimality of an adaptive mixed finite elementmethod using Raviart–Thomas or Brezzi–Douglas–Marini elements for Poisson’s equationon contractible domains in R^2, which can be viewed as a boundary problem on the deRham complex. Recently Demlow and Hirani (Found. Math. Comput. 14 (2014) 1337–1371) developed fundamental tools for a posteriori analysis on the de Rham *** this paper, we use tools in FEEC to construct convergence and complexity resultson domains with general topology and spatial dimension. In particular, we construct areliable and efficient error estimator and a sharper quasi-orthogonality result using a noveltechnique. Without marking for data oscillation, our adaptive method is a contractionwith respect to a total error incorporating the error estimator and data oscillation.
维普期刊数据库