An overview of the discontinuous Petrov Galerkin method

LF Demkowicz, J Gopalakrishnan - Recent Developments in …, 2014‏ - Springer
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[كتاب][B] Variational multiscale stabilization and the exponential decay of fine-scale correctors

D Peterseim - 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 …

Adaptive Petrov--Galerkin methods for first order transport equations

W Dahmen, C Huang, C Schwab, G Welper - SIAM journal on numerical …, 2012‏ - SIAM
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 …

High-performance finite elements with MFEM

J Andrej, N Atallah, JP Bäcker… - … Journal of High …, 2024‏ - journals.sagepub.com
The MFEM (Modular Finite Element Methods) library is a high-performance C++ library for
finite element discretizations. MFEM supports numerous types of finite element methods and …

A class of discontinuous Petrov–Galerkin methods. Part III: Adaptivity

L Demkowicz, J Gopalakrishnan, AH Niemi - Applied numerical …, 2012‏ - Elsevier
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 …

[كتاب][B] Multiscale Model Reduction

E Chung, Y Efendiev, TY Hou - 2023‏ - Springer
The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modeling and the …

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 …

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 …

[HTML][HTML] A robust DPG method for convection-dominated diffusion problems II: Adjoint boundary conditions and mesh-dependent test norms

J Chan, N Heuer, T Bui-Thanh, L Demkowicz - Computers & Mathematics …, 2014‏ - Elsevier
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 …

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 …