7 papers · 1 filter
Do locking-free finite element schemes lock for holey Reissner-Mindlin plates with mixed boundary conditions?
Mark Ainsworth, Charles Parker
We revisit finite element discretizations of the Reissner-Mindlin plate in the case of non-simply connected (holey) domains with mixed boundary conditions. Guided by the de Rham co…
Two and three dimensional -conforming finite element approximations without -elements
Mark Ainsworth, Charles Parker
We develop a method to compute -conforming finite element approximations in both two and three space dimensions using readily available finite element spaces. This is accompli…
Computing -conforming finite element approximations without having to implement -elements
Mark Ainsworth, Charles Parker
We develop a method to compute the -conforming finite element approximation to planar fourth order elliptic problems without having to implement elements. The algorithm…
Stable Lifting of Polynomial Traces on Triangles
Charles Parker, Endre Süli
We construct a right inverse of the trace operator on the reference triangle that maps suitable piecewise polynomial d…
Uniform Preconditioners for High Order Finite Element Approximations of Planar Linear Elasticity
Mark Ainsworth, Charles Parker
A new preconditioner is developed for high order finite element approximation of linear elastic problems on triangular meshes in two dimensions. The new preconditioner results in a…
Statically Condensed Iterated Penalty Method for High Order Finite Element Discretizations of Incompressible Flow
Mark Ainsworth, Charles Parker
We introduce and analyze a Statically Condensed Iterated Penalty (SCIP) method for solving incompressible flow problems discretized with th-order Scott-Vogelius elements. While…