Analysis of the DPG method for the Poisson equation

L Demkowicz, J Gopalakrishnan - SIAM Journal on Numerical Analysis, 2011 - SIAM
… is to give a few new techniques to analyze DPG methods for problems in … Poisson equation,
we are not advocating that one should use the DPG method for the simple Poisson equation (…

An analysis of the practical DPG method

J Gopalakrishnan, W Qiu - Mathematics of Computation, 2014 - ams.org
… the discontinuous Petrov-Galerkin (DPG) method applied to the Laplace equation and the …
, we perform the error analysis for the practical DPG method for the Laplace equation. We also …

[PDF][PDF] Analysis of the DPG method for the Poisson equation

L Demkowicz, J Gopalakrishnan - 2010 - conservancy.umn.edu
… an analysis of a discontinuous Petrov-Galerkin (DPG) method for a simple model problem
involving the Poisson equation… a few new techniques to analyze DPG methods for problems in …

Wavenumber explicit analysis of a DPG method for the multidimensional Helmholtz equation

L Demkowicz, J Gopalakrishnan, I Muga… - Computer Methods in …, 2012 - Elsevier
… Petrov Galerkin (DPG) method for the Helmholtz equation. We analyze the method and give
… The details of the derivation are very similar to the case of the Poisson equation [6], so we …

A spacetime DPG method for the Schrodinger equation

L Demkowicz, J Gopalakrishnan, S Nagaraj… - … on Numerical Analysis, 2017 - SIAM
… The convergence of the DPG method based on the ultraweak formulation is investigated
using an interpolation operator. A stand-alone appendix analyzes the ultraweak formulation for …

An implicit-in-time DPG formulation of the 1D1V Vlasov-Poisson equations

NV Roberts, ST Miller, SD Bond, EC Cyr - Computers & Mathematics with …, 2024 - Elsevier
… specify the DPG formulations for the Vlasov and Poisson equations, and the approach we
… Here, we offer a brief summary of the DPG method. For a fuller introduction, see the original …

[HTML][HTML] Low-order dPG-FEM for an elliptic PDE

C Carstensen, D Gallistl, F Hellwig… - Computers & Mathematics …, 2014 - Elsevier
… –Galerkin (dPG) finite element method (FEM) for the Poisson model … This lowest-order
discretization for the Poisson model … the numerical analysis of the dPG finite element method. The …

Using a DPG method to validate DMA experimental calibration of viscoelastic materials

F Fuentes, L Demkowicz, A Wilder - … Methods in Applied Mechanics and …, 2017 - Elsevier
… a DPG method. Second, it is to use such an implementation to validate calibration data directly
from dynamic mechanical analysis (… trait of the general DPG methodology which can be …

A unified discontinuous Petrov--Galerkin method and its analysis for Friedrichs' systems

T Bui-Thanh, L Demkowicz, O Ghattas - SIAM Journal on Numerical Analysis, 2013 - SIAM
… s equations. The results show that we not only recover several existing DPG methods, but also
discover new DPG methods … identical to those analyzed in [14] for the Poisson equation if f …

A posteriori error control for DPG methods

C Carstensen, L Demkowicz, J Gopalakrishnan - … on Numerical Analysis, 2014 - SIAM
… The first experiment solves the DPG method for the Laplace equation on the unit square
with load set so that the exact solution is u = sin(πx1) sin(πx2). For a series of successive …