Minimal residual methods in negative or fractional Sobolev norms
DOI10.1090/mcom/3904arXiv2301.10484OpenAlexW4387096997MaRDI QIDQ6122175
Harald Monsuur, Johannes Storn, Rob P. Stevenson
Publication date: 28 February 2024
Published in: Mathematics of Computation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2301.10484
a posteriori error estimatorinhomogeneous boundary conditionsquasi-optimal approximationleast squares methodsFortin operator
Stability in context of PDEs (35B35) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) A priori estimates in context of PDEs (35B45) Iterative numerical methods for linear systems (65F10)
Related Items (1)
Cites Work
- Wavenumber explicit analysis of a DPG method for the multidimensional Helmholtz equation
- Least-squares finite element methods
- Least-quares for second-order elliptic problems
- Multigrid in H(div) and H(curl)
- Uniform preconditioners for problems of positive order
- Minimal residual space-time discretizations of parabolic equations: asymmetric spatial operators
- Operator preconditioning
- A robust Petrov-Galerkin discretisation of convection-diffusion equations
- The $L^2$-Projection and Quasi-Optimality of Galerkin Methods for Parabolic Equations
- Quasi-optimal Adaptive Pseudostress Approximation of the Stokes Equations
- An analysis of the practical DPG method
- A class of discontinuous Petrov-Galerkin methods. II. Optimal test functions
- Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
- A Uniformly Accurate Finite Element Method for the Reissner–Mindlin Plate
- Multilevel Boundary Functionals for Least-Squares Mixed Finite Element Methods
- A least-squares approach based on a discrete minus one inner product for first order systems
- Preconditioning in H(𝑑𝑖𝑣) and applications
- Stability of Galerkin discretizations of a mixed space–time variational formulation of parabolic evolution equations
- Further results on a space-time FOSLS formulation of parabolic PDEs
- Multilevel decompositions and norms for negative order Sobolev spaces
- Equivalence of local- and global-best approximations, a simple stable local commuting projector, and optimal hp approximation estimates in H (div)
- How to Prove the Discrete Reliability for Nonconforming Finite Element Methods
- Uniform preconditioners for problems of negative order
- A Posteriori Error Control for DPG Methods
- Nodal Auxiliary Space Preconditioning in H(curl) and H(div) Spaces
- First-order system least squares with inhomogeneous boundary conditions
- MINRES for Second-Order PDEs with Singular Data
- Interpolation operator on negative Sobolev spaces
- A pollution-free ultra-weak FOSLS discretization of the Helmholtz equation
This page was built for publication: Minimal residual methods in negative or fractional Sobolev norms