Discretization of Linear Problems in Banach Spaces: Residual Minimization, Nonlinear Petrov--Galerkin, and Monotone Mixed Methods

DOI10.1137/20M1324338zbMath1457.65024arXiv1511.04400MaRDI QIDQ3386990

Ignacio Muga, Kristoffer G. Van Der Zee

Publication date: 12 January 2021

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.04400

zbMATH Keywords

duality mappingerror analysisbest approximationquasi-optimalityresidual minimizationPetrov-Galerkin discretizationoperators in Banach spaces

Mathematics Subject Classification ID

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) Geometry and structure of normed linear spaces (46B20) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Numerical solutions to equations with linear operators (65J10)

Related Items (13)

Gibbs phenomena for L^q-best approximation in finite element spaces ⋮ Projection in negative norms and the regularization of rough linear functionals ⋮ An \(L^p\)-DPG method with application to 2D convection-diffusion problems ⋮ Neural control of discrete weak formulations: Galerkin, least squares \& minimal-residual methods with quasi-optimal weights ⋮ Automatic stabilization of finite-element simulations using neural networks and hierarchical matrices ⋮ Filtering for Anderson Acceleration ⋮ Solving minimal residual methods in \(W^{-1,p'}\) with large exponents \(p\) ⋮ A DPG method for planar div-curl problems ⋮ An \(L^p\)-DPG method for the convection-diffusion problem ⋮ A machine-learning minimal-residual (ML-MRes) framework for goal-oriented finite element discretizations ⋮ The convection-diffusion-reaction equation in non-Hilbert Sobolev spaces: a direct proof of the inf-sup condition and stability of Galerkin's method ⋮ The discrete-dual minimal-residual method (DDMRES) for weak advection-reaction problems in Banach spaces ⋮ Camellia: a rapid development framework for finite element solvers

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