3 papers
math.NA2023
Preserving Superconvergence of Spectral Elements for Curved Domains via and -Geometric Refinement
Jacob Jones, Rebecca Conley, Xiangmin Jiao
Spectral element methods (SEM), which are extensions of finite element methods (FEM), are important emerging techniques for solving partial differential equations in physics and en…
math.NA2016
A Hybrid Method and Unified Analysis of Generalized Finite Differences and Lagrange Finite Elements
Rebecca Conley, Xiangmin Jiao, Tristan J. Delaney
Finite differences, finite elements, and their generalizations are widely used for solving partial differential equations, and their high-order variants have respective advantages…
math.NA2015
Overcoming Element Quality Dependence of Finite Elements with Adaptive Extended Stencil FEM (AES-FEM)
Rebecca Conley, Tristan J. Delaney, Xiangmin Jiao
The finite element methods (FEM) are important techniques in engineering for solving partial differential equations, but they depend heavily on element shape quality for stability…