17 citations · 27 across the 5 of their papers we have counts for
5 papers
Direct Serendipity and Mixed Finite Elements on Convex Polygons
Todd Arbogast, Chuning Wang
We construct new families of direct serendipity and direct mixed finite elements on general planer convex polygons that are and conforming, respectively, and possess…
A Direct Mixed-Enriched Galerkin Method on Quadrilaterals for Two-phase Darcy Flow
Todd Arbogast, Zhen Tao
We develop a locally conservative, finite element method for simulation of two-phase flow on quadrilateral meshes that minimize the number of degrees of freedom (DoFs) subject to a…
Direct Serendipity and Mixed Finite Elements on Convex Quadrilaterals
Todd Arbogast, Zhen Tao
The classical serendipity and mixed finite element spaces suffer from poor approximation on nondegenerate, convex quadrilaterals. In this paper, we develop $\textit{direct serendip…
A Hybridized Discontinuous Galerkin Method for A Linear Degenerate Elliptic Equation Arising from Two-Phase Mixtures
Shinhoo Kang, Tan Bui-Thanh, Todd Arbogast
We develop a high-order hybridized discontinuous Galerkin (HDG) method for a linear degenerate elliptic equation arising from a two-phase mixture of mantle convection or glacier dy…
Construction of -Conforming Mixed Finite Elements on Cuboidal Hexahedra
Todd Arbogast, Zhen Tao
We generalize the two dimensional mixed finite elements of Arbogast and Correa [T. Arbogast and M. R. Correa, SIAM J. Numer. Anal., 54 (2016), pp. 3332--3356] defined on quadrilate…