8 papers
Nonconforming virtual element method for the Monge-Ampère equation
Scott Congreve, Alice Hodson, Anwesh Pradhan
In this article, we develop the -nonconforming -conforming virtual element method (VEM) for the vanishing moment approximation of the second-order fully nonlinear Monge-A…
A posteriori error analysis of the virtual element method for second-order quasilinear elliptic PDEs
Scott Congreve, Alice Hodson
In this paper we develop a -conforming virtual element method (VEM) for a class of second-order quasilinear elliptic PDEs in two dimensions. We present a posteriori error anal…
Goal-oriented error analysis of iterative Galerkin discretizations for nonlinear problems including linearization and algebraic errors
Vit Dolejsi, Scott Congreve
We consider the goal-oriented error estimates for a linearized iterative solver for nonlinear partial differential equations. For the adjoint problem and iterative solver we consid…
Two-grid -version discontinuous Galerkin finite element methods for quasilinear elliptic PDEs on agglomerated coarse meshes
Scott Congreve, Paul Houston
This article considers the extension of two-grid -version discontinuous Galerkin finite element methods for the numerical approximation of second-order quasilinear elliptic bou…
Robust adaptive hp discontinuous Galerkin finite element methods for the Helmholtz equation
Scott Congreve, Joscha Gedicke, Ilaria Perugia
This paper presents an a posteriori error analysis for the 2D Helmholtz equation that is robust in the polynomial degree and the wave number . For the discretization, w…
Numerical investigation of the conditioning for plane wave discontinuous Galerkin methods
Scott Congreve, Joscha Gedicke, Ilaria Perugia
We present a numerical study to investigate the conditioning of the plane wave discontinuous Galerkin discretization of the Helmholtz problem. We provide empirical evidence that th…
Adaptive Refinement for -Version Trefftz Discontinuous Galerkin Methods for the Homogeneous Helmholtz Problem
Scott Congreve, Paul Houston, Ilaria Perugia
In this article we develop an -adaptive refinement procedure for Trefftz discontinuous Galerkin methods applied to the homogeneous Helmholtz problem. Our approach combines not…
Iterative Galerkin Discretizations for Strongly Monotone Problems
Scott Congreve, Thomas P. Wihler
In this article we investigate a finite element formulation of strongly monotone quasi-linear elliptic PDEs in the context of fixed-point iterations. As opposed to Newton's method,…