A class of Bernstein-Bézier basis based high-order finite element methods is developed for
the Galerkin-characteristics solution of convection-diffusion problems. The Galerkin …

This work presents a comprehensive discretization theory for abstract linear operator
equations in Banach spaces. The fundamental starting point of the theory is the idea of …

We present a high-order Bernstein–Bézier finite element discretization to accurately solve
three-dimensional advection-dominated problems on unstructured tetrahedral meshes. The …

In this article, we study the spectral volume (SV) methods for scalar hyperbolic conservation
laws with a class of subdivision points under the Petrov–Galerkin framework. Due to the …

In this dissertation, we present a scalable parallel version of hp3D—a finite element (FE)
software for analysis and discretization of complex three-dimensional multiphysics …

An adaptive enriched semi-Lagrangian finite element method is proposed for the numerical
solution of coupled flow-transport problems on unstructured triangular meshes. The new …

This paper aims to develop a semi-Lagrangian Bernstein–Bézier high-order finite element
method for solving the two-dimensional nonlinear coupled Burgers' equations at high …

We propose a mass-conservative and monotonicity-preserving characteristic finite element
method for solving three-dimensional transport and incompressible Navier-Stokes equations …

A direct approach is developed using Streamline Upwind Petrov Galerkin (SUPG) concepts
to determine the spatially varying property distribution in a nominally heterogeneous …

We consider quasi-polynomial spaces of differential forms defined as weighted (with a
positive weight) spaces of differential forms with polynomial coefficients. We show that the …