An overview of the discontinuous Petrov Galerkin method
LF Demkowicz, J Gopalakrishnan - Recent Developments in …, 2014 - Springer
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Variational multiscale stabilization and the exponential decay of fine-scale correctors
D Peterseim - Building bridges: connections and challenges in …, 2016 - Springer
This paper reviews the variational multiscale stabilization of standard finite element methods
for linear partial differential equations that exhibit multiscale features. The stabilization is of …
for linear partial differential equations that exhibit multiscale features. The stabilization is of …
Adaptive Petrov--Galerkin methods for first order transport equations
We propose stable variational formulations for certain linear, unsymmetric operators with first
order transport equations in bounded domains serving as the primary focus of this paper …
order transport equations in bounded domains serving as the primary focus of this paper …
A class of discontinuous Petrov–Galerkin methods. Part III: Adaptivity
We continue our theoretical and numerical study on the Discontinuous Petrov–Galerkin
method with optimal test functions in context of 1D and 2D convection-dominated diffusion …
method with optimal test functions in context of 1D and 2D convection-dominated diffusion …
Analysis of the DPG method for the Poisson equation
L Demkowicz, J Gopalakrishnan - SIAM Journal on Numerical Analysis, 2011 - SIAM
We give an error analysis of the recently developed DPG method applied to solve the
Poisson equation and a convection-diffusion problem. We prove that the method is …
Poisson equation and a convection-diffusion problem. We prove that the method is …
Robust DPG method for convection-dominated diffusion problems
L Demkowicz, N Heuer - SIAM Journal on Numerical Analysis, 2013 - SIAM
We propose and analyze a discontinuous Petrov--Galerkin (DPG) method for convection-
dominated diffusion problems that provides robust L^2 error estimates for the field variables …
dominated diffusion problems that provides robust L^2 error estimates for the field variables …
[HTML][HTML] A robust DPG method for convection-dominated diffusion problems II: Adjoint boundary conditions and mesh-dependent test norms
We introduce a DPG method for convection-dominated diffusion problems. The choice of a
test norm is shown to be crucial to achieving robust behavior with respect to the diffusion …
test norm is shown to be crucial to achieving robust behavior with respect to the diffusion …
Eliminating the pollution effect in Helmholtz problems by local subscale correction
D Peterseim - Mathematics of Computation, 2017 - ams.org
We introduce a new Petrov-Galerkin multiscale method for the numerical approximation of
the Helmholtz equation with large wave number $\kappa $ in bounded domains in $\mathbb …
the Helmholtz equation with large wave number $\kappa $ in bounded domains in $\mathbb …
Double greedy algorithms: Reduced basis methods for transport dominated problems∗
The central objective of this paper is to develop reduced basis methods for parameter
dependent transport dominated problems that are rigorously proven to exhibit rate-optimal …
dependent transport dominated problems that are rigorously proven to exhibit rate-optimal …
Pre-asymptotic error analysis of CIP-FEM and FEM for the Helmholtz equation with high wave number. Part I: linear version
H Wu - IMA Journal of Numerical Analysis, 2014 - academic.oup.com
Ever since the pioneering work of Ihlenburg and Babuška for the one-dimensional
Helmholtz equation (1995, Comput. Math. Appl., 30, 9–37), a lot of pre-asymptotic analyses …
Helmholtz equation (1995, Comput. Math. Appl., 30, 9–37), a lot of pre-asymptotic analyses …