On a relation of discontinuous Petrov-Galerkin and least-squares finite element methods
DOI10.1016/j.camwa.2020.02.018zbMath1446.65180OpenAlexW3011239469MaRDI QIDQ2192533
Publication date: 17 August 2020
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.camwa.2020.02.018
Linear elasticity with initial stresses (74B10) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical computation of matrix norms, conditioning, scaling (65F35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)
Related Items (3)
Cites Work
- Unnamed Item
- A robust DPG method for convection-dominated diffusion problems. II: Adjoint boundary conditions and mesh-dependent test norms
- The DPG method for the Stokes problem
- A class of discontinuous Petrov-Galerkin methods. III: Adaptivity
- Breaking spaces and forms for the DPG method and applications including Maxwell equations
- A class of discontinuous Petrov-Galerkin methods. IV: The optimal test norm and time-harmonic wave propagation in 1D
- A class of discontinuous Petrov-Galerkin methods. I: The transport equation
- A locking-free \(hp\) DPG method for linear elasticity with symmetric stresses
- An optimal Poincaré inequality for convex domains
- Locking effects in the finite element approximation of elasticity problems
- Nonlinear discontinuous Petrov-Galerkin methods
- A low-order discontinuous Petrov-Galerkin method for the Stokes equations
- An adaptive DPG method for high frequency time-harmonic wave propagation problems
- On traces for \(\mathbf H(\text{curl},\Omega)\) in Lipschitz domains.
- The DPG methodology applied to different variational formulations of linear elasticity
- A discontinuous Petrov-Galerkin methodology for adaptive solutions to the incompressible Navier-Stokes equations
- Low-order dPG-FEM for an elliptic PDE
- On traces for functional spaces related to Maxwell's equations Part I: An integration by parts formula in Lipschitz polyhedra
- A Unified Discontinuous Petrov--Galerkin Method and Its Analysis for Friedrichs' Systems
- An analysis of the practical DPG method
- A class of discontinuous Petrov-Galerkin methods. II. Optimal test functions
- Analysis of the DPG Method for the Poisson Equation
- 3. A space-time discontinuous Petrov–Galerkin method for acoustic waves
- On Locking and Robustness in the Finite Element Method
- Asymptotic Exactness of the Least-Squares Finite Element Residual
- Least-Squares Methods for Linear Elasticity
- A Spacetime DPG Method for the Schrödinger Equation
- Computation of the LBB Constant for the Stokes Equation with a Least-Squares Finite Element Method
- A Robust DPG Method for Singularly Perturbed Reaction-Diffusion Problems
- Dispersive and Dissipative Errors in the DPG Method with Scaled Norms for Helmholtz Equation
- Low-Order Discontinuous Petrov--Galerkin Finite Element Methods for Linear Elasticity
This page was built for publication: On a relation of discontinuous Petrov-Galerkin and least-squares finite element methods