A superconvergent finite element scheme for the Reissner-Mindlin plate by projection methods
Junping Wang 1, Xiu Ye 21 Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, CO 80401, USA
2 Department of Mathematics and Statistics, University of Arkansas at Little Rock, 2801 South University, Little Rock, Arkansas 72204, USA
Received by the editors January 27, 2004.
The Reissner-Mindlin model is frequently used by engineers for plates and shells of small to moderate thickness. This model is well known for its "locking" phenomenon so that many numerical approximations behave poorly when the thickness parameter tends to zero. Following the formulation derived by Brezzi and Fortin, we construct a new finite element scheme for the Reissner-Mindlin model using L^2 projections onto appropriately-chosen finite element spaces. A superconvergence result is established for the new finite element solutions by using the L^2 projections. The superconvergence is based on some regularity assumption for the Reissner-Mindlin model and is applicable to any stable finite element methods with regular but non-uniform finite element partitions.AMS subject classifications: 65F10, 65F30
Key words: finite element methods, superconvergence, the method of least-squares fitting, Reissner-Mindlin plate
Email: firstname.lastname@example.org (J. Wang), email@example.com (X. Ye)