American Institute of Mathematical Sciences

October  2010, 26(4): 1305-1318. doi: 10.3934/dcds.2010.26.1305

Maximum norm error estimates for Div least-squares method for Darcy flows

 1 Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, United States

Received  November 2008 Revised  April 2009 Published  December 2009

Least-squares finite element methods for second order elliptic partial differential equations such as Darcy flows are considered. While there has been a significant progress in terms of obtaining error estimates for the methods, the estimates are essentially based on $L_2$-norm of the error. In this paper, we provide maximum norm error estimates for the primary variable using a smoothed Green's function introduced in [33] and maximum norm error for the dual variables by taking advantage of the fact that least-squares solutions are higher-order perturbations of Galerkin solutions [8].
Citation: JaEun Ku. Maximum norm error estimates for Div least-squares method for Darcy flows. Discrete & Continuous Dynamical Systems - A, 2010, 26 (4) : 1305-1318. doi: 10.3934/dcds.2010.26.1305
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