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An overview of the discontinuous Petrov Galerkin method
An Overview of the Discontinuous Petrov Galerkin Method | SpringerLink Skip to main content
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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 …
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 …
High-performance finite elements with MFEM
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 …
finite element discretizations. MFEM supports numerous types of finite element methods and …
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 …
[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 …
impact of computer technology, the growing importance of computer modeling and the …
Analysis of the DPG method for the Poisson equation
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
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
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 …