Improved rates for a space-time FOSLS of parabolic PDEs

DOI10.1007/s00211-023-01387-3arXiv2208.10824OpenAlexW4390264332MaRDI QIDQ6191367

Rob P. Stevenson, Gregor Gantner

Publication date: 9 February 2024

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2208.10824

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical methods for initial value problems involving ordinary differential equations (65L05) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Systems of linear first-order PDEs (35F35)

Cites Work

• Unnamed Item
• Unnamed Item
• Space-time finite element methods for parabolic problems
• A space-time DPG method for the heat equation
• Least-squares finite element methods
• Generalized finite element systems for smooth differential forms and Stokes' problem
• An optimal adaptive wavelet method for first order system least squares
• Space-time least-squares finite elements for parabolic equations
• A wavelet-in-time, finite element-in-space adaptive method for parabolic evolution equations
• Application of a minimal compatible element to incompressible and nearly incompressible continuum mechanics
• Minimal residual space-time discretizations of parabolic equations: asymmetric spatial operators
• Space-time isogeometric analysis of parabolic evolution problems
• Two-grid finite-element schemes for the transient Navier-Stokes problem
• Mixed and Hybrid Finite Element Methods
• hp-Approximation Theory forBDFMandRTFinite Elements on Quadrilaterals
• Stability of sparse space-time finite element discretizations of linear parabolic evolution equations
• Stability of Galerkin discretizations of a mixed space–time variational formulation of parabolic evolution equations
• Finite Elements I
• Further results on a space-time FOSLS formulation of parabolic PDEs
• A Well-Posed First Order System Least Squares Formulation of the Instationary Stokes Equations
• Finite element quasi-interpolation and best approximation
• The completion of locally refined simplicial partitions created by bisection