Efficient discretization and preconditioning of the singularly perturbed reaction-diffusion problem
DOI10.1016/j.camwa.2022.01.031OpenAlexW4220997604MaRDI QIDQ2667979
Constantin Bacuta, Daniel Hayes, Jacob Jacavage
Publication date: 2 March 2022
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2104.11337
preconditioningleast squaresmixed methodssaddle point systemsoptimal test normUzawa conjugate gradient
Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Boundary value problems for second-order elliptic equations (35J25) 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) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Multilevel preconditioners for reaction-diffusion problems with discontinuous coefficients
- A robust DPG method for convection-dominated diffusion problems. II: Adjoint boundary conditions and mesh-dependent test norms
- Multilevel discretization of symmetric saddle point systems without the discrete LBB condition
- Breaking spaces and forms for the DPG method and applications including Maxwell equations
- A class of discontinuous Petrov-Galerkin methods. I: The transport equation
- Saddle point least squares for the reaction-diffusion problem
- Layer-adapted meshes and FEM for time-dependent singularly perturbed reaction-diffusion problems
- Schur complements on Hilbert spaces and saddle point systems
- \(hp\)-finite element methods for singular perturbations
- Modeling of electromagnetic absorption/scattering problems using \(hp\)-adaptive finite elements
- A saddle point least squares approach to mixed methods
- A saddle point least squares approach for primal mixed formulations of second order PDEs
- Notes on a saddle point reformulation of mixed variational problems
- Saddle point least squares preconditioning of mixed methods
- Singularly perturbed reaction-diffusion problems as first order systems
- A non-conforming saddle point least squares approach for an elliptic interface problem
- Convergence rates of the DPG method with reduced test space degree
- A robust Petrov-Galerkin discretisation of convection-diffusion equations
- Adaptivity and variational stabilization for convection-diffusion equations
- Robust Solution of Singularly Perturbed Problems Using Multigrid Methods
- A class of discontinuous Petrov-Galerkin methods. II. Optimal test functions
- Convergence and stability in balanced norms of finite element methods on Shishkin meshes for reaction‐diffusion problems
- Parallel Multilevel Preconditioners
- Optimal Petrov—Galerkin Methods through Approximate Symmetrization
- A first-order system Petrov–Galerkin discretization for a reaction–diffusion problem on a fitted mesh
- A Balanced Finite Element Method for Singularly Perturbed Reaction-Diffusion Problems
- Computational scales of Sobolev norms with application to preconditioning
- A Dual Finite Element Method for a Singularly Perturbed Reaction-Diffusion Problem
- Least squares preconditioning for mixed methods with nonconforming trial spaces
- A parameter robust numerical method for a two dimensional reaction-diffusion problem
- Convergence and superconvergence analysis of finite element methods on highly nonuniform anisotropic meshes for singularly perturbed reaction-diffusion problems
This page was built for publication: Efficient discretization and preconditioning of the singularly perturbed reaction-diffusion problem
