ELLAM for resolving the kinematics of two-dimensional resistive magnetohydrodynamic flows. - Jiangguo Liu; Simon Tavener; Hongsen Chen (J. Comput. Phys., 2007)

A Posteriori Analysis and Adaptive Error Control for Multiscale Operator Decomposition Solution of Elliptic Systems I: Triangular Systems. - Varis Carey; Donald J. Estep; Simon Tavener (SIAM J. Numer. Anal., 2008)

An A Posteriori-A Priori Analysis of Multiscale Operator Splitting. - Donald J. Estep; Victor Ginting; David L. Ropp; John N. Shadid; Simon Tavener (SIAM J. Numer. Anal., 2008)

A Posteriori Analysis and Improved Accuracy for an Operator Decomposition Solution of a Conjugate Heat Transfer Problem. - Donald J. Estep; Simon Tavener; Tim Wildey (SIAM J. Numer. Anal., 2008)

A posteriori error analysis of a cell-centered finite volume method for semilinear elliptic problems. - Donald J. Estep; Michael Pernice; Du Pham; Simon Tavener; Haiying Wang (J. Comput. Appl. Math., 2009)

Nonparametric Density Estimation for Randomly Perturbed Elliptic Problems I: Computational Methods, A Posteriori Analysis, and Adaptive Error Control. - Donald J. Estep; Axel Målqvist; Simon Tavener (SIAM J. Sci. Comput., 2009)

A posteriori error estimation and adaptive mesh refinement for a multiscale operator decomposition approach to fluid-solid heat transfer. - Donald J. Estep; Simon Tavener; Tim Wildey (J. Comput. Phys., 2010)

Blockwise Adaptivity for Time Dependent Problems Based on Coarse Scale Adjoint Solutions. - Varis Carey; Donald J. Estep; August Johansson; Mats G. Larson; Simon Tavener (SIAM J. Sci. Comput., 2010)

A Mathematical Model for Intracellular HIV-1 Gag Protein Transport and its Parallel Numerical Simulations. - Jiangguo Liu; Roberto Muñoz-Alicea; Tingwen Huang; Simon Tavener; Chaoping Chen (ICCS, 2012)

Adjoint-Based a Posteriori Error Estimation for Coupled Time-Dependent Systems. - Liya Asner; Simon Tavener; David Kay (SIAM J. Sci. Comput., 2012)

Adjoint Based A Posteriori Analysis of Multiscale Mortar Discretizations with Multinumerics. - Simon Tavener; Tim Wildey (SIAM J. Sci. Comput., 2013)

A posteriori error estimation for the Lax-Wendroff finite difference scheme. - James B. Collins; Donald J. Estep; Simon Tavener (J. Comput. Appl. Math., 2014)

A Measure-Theoretic Computational Method for Inverse Sensitivity Problems III: Multiple Quantities of Interest. - Troy D. Butler; Donald J. Estep; Simon Tavener; Clint Dawson 001; Joannes J. Westerink (SIAM/ASA J. Uncertain. Quantification, 2014)

A Posteriori Error Estimates for Mixed Finite Element and Finite Volume Methods for Parabolic Problems Coupled through a Boundary. - Todd Arbogast; Donald J. Estep; Brendan Sheehan; Simon Tavener (SIAM/ASA J. Uncertain. Quantification, 2015)

A Posteriori Analysis for Iterative Solvers for Nonautonomous Evolution Problems. - Jehanzeb Hameed Chaudhry; Donald J. Estep; Victor Ginting; Simon Tavener (SIAM/ASA J. Uncertain. Quantification, 2015)

Stabilized Lowest-Order Finite Element Approximation for Linear Three-Field Poroelasticity. - Lorenz Berger; Rafel Bordas; David Kay; Simon Tavener (SIAM J. Sci. Comput., 2015)

A Posteriori Error Analysis of Two-Stage Computation Methods with Application to Efficient Discretization and the Parareal Algorithm. - Jehanzeb Hameed Chaudhry; Donald J. Estep; Simon Tavener; Varis Carey; Jeff Sandelin (SIAM J. Numer. Anal., 2016)

A Two-Field Finite Element Solver for Poroelasticity on Quadrilateral Meshes. - Graham Harper; Jiangguo Liu; Simon Tavener; Zhuoran Wang (ICCS (3), 2018)

The lowest-order weak Galerkin finite element method for the Darcy equation on quadrilateral and hybrid meshes. - Jiangguo Liu; Simon Tavener; Zhuoran Wang (J. Comput. Phys., 2018)

Lowest-Order Weak Galerkin Finite Element Method for Darcy Flow on Convex Polygonal Meshes. - Jiangguo Liu; Simon Tavener; Zhuoran Wang (SIAM J. Sci. Comput., 2018)

deal.II Implementation of a Weak Galerkin Finite Element Solver for Darcy Flow. - Zhuoran Wang; Graham Harper; Patrick O'Leary; Jiangguo Liu; Simon Tavener (ICCS (4), 2019)

A posteriori error analysis for Schwarz overlapping domain decomposition methods. - Jehanzeb Hameed Chaudhry; Donald J. Estep; Simon Tavener (CoRR, 2019)

Lowest-Order Weak Galerkin Finite Element Methods for Linear Elasticity on Rectangular and Brick Meshes. - Graham Harper; Jiangguo Liu; Simon Tavener; Bin Zheng (J. Sci. Comput., 2019)

A locking-free solver for linear elasticity on quadrilateral and hexahedral meshes based on enrichment of Lagrangian elements. - Graham Harper; Ruishu Wang; Jiangguo Liu; Simon Tavener; Ran Zhang 002 (Comput. Math. Appl., 2020)

Error estimation and uncertainty quantification for first time to a threshold value. - Jehanzeb H. Chaudhry; Donald J. Estep; Zachary Stevens; Simon J. Tavener (CoRR, 2020)

A lowest-order weak Galerkin finite element method for Stokes flow on polygonal meshes. - Jiangguo Liu; Graham Harper; Nolisa Malluwawadu; Simon Tavener (J. Comput. Appl. Math., 2020)

Penalty-Free Any-Order Weak Galerkin FEMs for Elliptic Problems on Quadrilateral Meshes. - Jiangguo Liu; Simon Tavener; Zhuoran Wang (J. Sci. Comput., 2020)

A posteriori error analysis for a space-time parallel discretization of parabolic partial differential equations. - Jehanzeb H. Chaudhry; Donald J. Estep; Simon Tavener (CoRR, 2021)

Error analysis of first time to a threshold value for partial differential equations. - Jehanzeb H. Chaudhry; Donald J. Estep; Trevor Giannini; Zachary Stevens; Simon Tavener (CoRR, 2021)

Analysis of a 2-field finite element solver for poroelasticity on quadrilateral meshes. - Zhuoran Wang; Simon Tavener; Jiangguo Liu (J. Comput. Appl. Math., 2021)

Understanding the impact of numerical solvers on inference for differential equation models. - Richard Creswell; Katherine M. Shepherd; Ben Lambert; Gary R. Mirams; Chon Lok Lei; Simon Tavener; Martin Robinson; David J. Gavaghan (CoRR, 2023)

Rethinking the Relationship between Recurrent and Non-Recurrent Neural Networks: A Study in Sparsity. - Quincy Hershey; Randy C. Paffenroth; Harsh Nilesh Pathak; Simon Tavener (CoRR, 2024)

Full weak Galerkin finite element discretizations for poroelasticity problems in the primal formulation. - Ruishu Wang; Zhuoran Wang; Simon Tavener; Jiangguo Liu (J. Comput. Appl. Math., 2024)