A least-squares formulation of the moving discontinuous Galerkin finite element method with interface condition enforcement
From MaRDI portal
Publication:2034894
DOI10.1016/j.camwa.2020.09.012OpenAlexW3006833264MaRDI QIDQ2034894
Andrew D. Kercher, Andrew Corrigan
Publication date: 23 June 2021
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2003.01044
Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element methods applied to problems in fluid mechanics (76M10)
Related Items
A moving discontinuous Galerkin finite element method with interface condition enforcement for compressible flows, Implicit shock tracking for unsteady flows by the method of lines, An adaptive viscosity regularization approach for the numerical solution of conservation laws: application to finite element methods, A space-time high-order implicit shock tracking method for shock-dominated unsteady flows, Editorial: Recent advances in least-squares and discontinuous Petrov-Galerkin finite element methods, High-order implicit shock tracking (HOIST)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- 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. I: The transport equation
- Implicit shock tracking using an optimization-based high-order discontinuous Galerkin method
- Least-squares finite element methods
- Layer-adapted meshes for reaction-convection-diffusion problems
- Layer-adapted meshes for convection-diffusion problems
- Thirty-six years of shock fitting.
- Analysis of a discontinuous least squares spectral element method
- A DPG method for steady viscous compressible flow
- A PDE-constrained optimization approach to the discontinuous Petrov-Galerkin method with a trust region inexact Newton-CG solver
- An optimization-based approach for high-order accurate discretization of conservation laws with discontinuous solutions
- The DPG-star method
- Discrete least-squares finite element methods
- A discontinuous Petrov-Galerkin methodology for adaptive solutions to the incompressible Navier-Stokes equations
- A Brief History of Shock-Fitting
- 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
- Adaptivity with moving grids
- On the Finite Element Method for Singularly Perturbed Reaction-Diffusion Problems in Two and One Dimensions
- An Algorithm for Least-Squares Estimation of Nonlinear Parameters
- Finite Element Methods of Least-Squares Type
- On best possible order of convergence estimates in the collocation method and Galerkin's method for singularly perturbed boundary value problems for systems of first-order ordinary differential equations
- Thehp finite element method for singularly perturbed problems in nonsmooth domains
- First-Order System Least Squares for Second-Order Partial Differential Equations: Part I
- Least-Squares Finite Element Approximations to Solutions of Interface Problems
- The $p$ and $hp$ versions of the finite element method for problems with boundary layers
- Boundary Layer Resolving Pseudospectral Methods for Singular Perturbation Problems
- The LBB condition in fractional Sobolev spaces and applications
- The partial differential equation ut + uux = μxx
- On a quasi-linear parabolic equation occurring in aerodynamics
- A method for the solution of certain non-linear problems in least squares
