Abstract
SummaryIn this paper, finite element superconvergence phenomenon based on centroidal Voronoi Delaunay tessellations (CVDT) in three‐dimensional space is investigated. The Laplacian operator with the Dirichlet boundary condition is considered. A modified superconvergence patch recovery (MSPR) method is established to overcome the influence of slivers on CVDT meshes. With these two key preconditions, a CVDT mesh and the MSPR, the gradients recovered from the linear finite element solutions have superconvergence in the l2 norm at nodes of a CVDT mesh for an arbitrary three‐dimensional bounded domain. Numerous numerical examples are presented to demonstrate this superconvergence property and good performance of the MSPR method. Copyright © 2016 John Wiley & Sons, Ltd.
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