Space-time finite element methods stabilized using bubble function spaces

DOI10.1080/00036811.2018.1522630zbMath1437.65145OpenAlexW2893430750WikidataQ96351652 ScholiaQ96351652MaRDI QIDQ5109254

Ioannis Toulopoulos

Publication date: 11 May 2020

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036811.2018.1522630

zbMATH Keywords

optimal convergence ratesbubble stabilizationparabolic initial-boundary value problemsspace-time finite element methods

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Variational methods applied to PDEs (35A15) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items

Numerical Solutions of Quasilinear Parabolic Problems by a Continuous Space-Time Finite Element Scheme ⋮ Enabling four-dimensional conformal hybrid meshing with cubic pyramids ⋮ Finite element approach to linear parabolic pointwise control problems of incomplete data

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On long time integration of the heat equation
• Space-time finite element methods for parabolic problems
• Mathematical aspects of discontinuous Galerkin methods.
• The boundary value problems of mathematical physics. Transl. from the Russian by Jack Lohwater
• A relationship between stabilized finite element methods and the Galerkin method with bubble functions
• The characteristic streamline diffusion method for the time-dependent incompressible Navier-Stokes equations
• Adaptive FETI-DP and BDDC methods with a generalized transformation of basis for heterogeneous problems
• Space-time finite element methods for elastodynamics: Formulations and error estimates
• Theory and practice of finite elements.
• Space-time isogeometric analysis of parabolic evolution problems
• Virtual bubbles and Galerkin-least-squares type methods (Ga.L.S.)
• Subgrid stabilization of Galerkin approximations of linear monotone operators
• Space-time adaptive wavelet methods for parabolic evolution problems
• Adaptive Wavelet Schemes for Parabolic Problems: Sparse Matrices and Numerical Results
• Multipatch Space-Time Isogeometric Analysis of Parabolic Diffusion Problems
• The h-p version of the finite element method for parabolic equations. Part I. The p-version in time
• Time discretization of parabolic problems by the discontinuous Galerkin method
• Space‐time oriented streamline diffusion methods for non‐linear conservation laws in one dimension
• Error Estimates and Automatic Time Step Control for Nonlinear Parabolic Problems, I
• Adaptive Finite Element Methods for Parabolic Problems IV: Nonlinear Problems
• Adaptive Finite Element Methods for Parabolic Problems V: Long-Time Integration
• Stability of sparse space-time finite element discretizations of linear parabolic evolution equations
• Interpolation of non-smooth functions on anisotropic finite element meshes
• Stabilization of Galerkin approximations of transport equations by subgrid modeling
• The h‐p version of the finite element method for parabolic equations. II. The h‐p version in time
• Galerkin time-stepping methods for nonlinear parabolic equations
• The Mathematical Theory of Finite Element Methods
• Galerkin Finite Element Methods for Parabolic Problems