Efficiency Based Adaptive Local Refinement for First-Order System Least-Squares Formulations

Abstract. In this paper, we propose new adaptive local refinement (ALR) strategies for firstorder system least-squares (FOSLS) finite element in conjunction with algebraic multigrid (AMG) methods in the context of nested iteration (NI). The goal is to reach a certain error tolerance with the least amount of computational cost and nearly uniform distribution of the error over all elements. To accomplish this, the refinement decision at each refinement level is determined based on optimizing efficiency measures that take into account both error reduction and computational cost. Two efficiency measures are discussed, predicted error reduction and predicted computational cost. These methods are first applied to a 2D Poisson problem with steep gradients and the results are compared with the threshold-based methods described in [16]. Next, these methods are applied to a 2D reduced model of the incompressible, resistive magnetohydrodynamic (MHD) equations. These equations are used to si...

• Type: Journal
• Year: 2011
• Where: SIAMSC
• Authors: J. H. Adler, Thomas A. Manteuffel, Stephen F. McCormick, J. W. Nolting, John Ruge, L. Tang
• Keywords: Adaptive Local Refinement, Computational Cost, Error Reduction, SIAMSC 2011