106 citations · 218 across the 20 of their papers we have counts for
11 papers · 1 filter
Extending FEniCS to Work in Higher Dimensions Using Tensor Product Finite Elements
Mark Loveland, Eirik Valseth, Matt Lukac +1
We present a method to extend the finite element library FEniCS to solve problems with domains in dimensions above three by constructing tensor product finite elements. This method…
A Stable Mixed FE Method for Nearly Incompressible Linear Elastostatics
Eirik Valseth, Albert Romkes, Austin R. Kaul +1
We present a new, stable, mixed finite element (FE) method for linear elastostatics of nearly incompressible solids. The method is the automatic variationally stable FE (AVS-FE) me…
An Adaptive Stable Space-Time FE Method for the Shallow Water Equations
Eirik Valseth, Clint Dawson
We consider the finite element (FE) approximation of the shallow water equations (SWE) by considering discretizations in which both space and time are established using an uncondit…
Discontinuous Galerkin methods for a dispersive wave hydro-sediment-morphodynamic model
Kazbek Kazhyken, Juha Videman, Clint Dawson
A dispersive wave hydro-sediment-morphodynamic model developed by complementing the shallow water hydro-sediment-morphodynamic (SHSM) equations with the dispersive term from the Gr…
Automatic Variationally Stable Analysis for Finite Element Computations: Transient Convection-Diffusion Problems
Eirik Valseth, Pouria Behnoudfar, Clint Dawson +1
We establish stable finite element (FE) approximations of convection-diffusion initial boundary value problems using the automatic variationally stable finite element (AVS-FE) meth…
Learning Quantities of Interest from Dynamical Systems for Observation-Consistent Inversion
Steven Mattis, Kyle Robert Steffen, Troy Butler +2
Dynamical systems arise in a wide variety of mathematical models from science and engineering. A common challenge is to quantify uncertainties on model inputs (parameters) that cor…
An Unconditionally Stable Space-Time FE Method for the Korteweg-de Vries Equation
Eirik Valseth, Clint Dawson
We introduce an unconditionally stable finite element (FE) method, the automatic variationally stable FE (AVS-FE) method for the numerical analysis of the Korteweg-de Vries (KdV) e…
Discontinuous Galerkin methods for a dispersive wave hydro-morphodynamic model with bed-load transport
Kazbek Kazhyken, Juha Videman, Clint Dawson
A dispersive wave hydro-morphodynamic model coupling the Green-Naghdi equations (the hydrodynamic part) with the sediment continuity Exner equation (the morphodynamic part) is pres…
Adaptive Total Variation Stable Local Timestepping for Conservation Laws
Maximilian Bremer, John Bachan, Cy Chan +1
This paper proposes a first-order total variation diminishing (TVD) treatment for coarsening and refining of local timestep size in response to dynamic local variations in wave spe…
Solving Stochastic Inverse Problems using Sigma-Algebras on Contour Maps
Troy Butler, Don Estep, Simon Tavener +3
We compute approximate solutions to inverse problems for determining parameters in differential equation models with stochastic data on output quantities. The formulation of the pr…
Adaptive Mesh Refinement for Storm Surge
Kyle T. Mandli, Clint N. Dawson
An approach to utilizing adaptive mesh refinement algorithms for storm surge modeling is proposed. Currently numerical models exist that can resolve the details of coastal regions…