Charles Parker

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20212025

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math.NA2023

Computing $H^{2}$ -conforming finite element approximations without having to implement $C^{1}$ -elements

Mark Ainsworth, Charles Parker

We develop a method to compute the $H^{2}$ -conforming finite element approximation to planar fourth order elliptic problems without having to implement $C^{1}$ elements. The algorithm…

math.NA2023

Stable Lifting of Polynomial Traces on Triangles

Charles Parker, Endre Süli

We construct a right inverse of the trace operator $u \mapsto (u ∣_{\partial T}, \partial_{n} u ∣_{\partial T})$ on the reference triangle $T$ that maps suitable piecewise polynomial d…

math.NA2023

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…

math.NA2023

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 $p$ th-order Scott-Vogelius elements. While…

Computing H2-conforming finite element approximations without having to implement C1-elements

Stable Lifting of Polynomial Traces on Triangles

Uniform Preconditioners for High Order Finite Element Approximations of Planar Linear Elasticity

Statically Condensed Iterated Penalty Method for High Order Finite Element Discretizations of Incompressible Flow

Computing $H^{2}$ -conforming finite element approximations without having to implement $C^{1}$ -elements