Stability of sparse space-time finite element discretizations of linear parabolic evolution equations
From MaRDI portal
Publication:4907968
DOI10.1093/imanum/drs014zbMath1262.65114OpenAlexW2006697861MaRDI QIDQ4907968
Publication date: 27 February 2013
Published in: IMA Journal of Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1093/imanum/drs014
convergencenumerical experimentsabstract linear parabolic evolution equationsgeneralized least squares solutionoverdetermined matrix-vector equationsparse space-time product tensor minimal residual Petrov-Galerkin method
Abstract parabolic equations (35K90) 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)
Related Items (44)
Space-time \(hp\)-approximation of parabolic equations ⋮ Analysis of backward Euler primal DPG methods ⋮ A wavelet-in-time, finite element-in-space adaptive method for parabolic evolution equations ⋮ A space-time DPG method for the heat equation ⋮ Numerical Solutions of Quasilinear Parabolic Problems by a Continuous Space-Time Finite Element Scheme ⋮ A Parallel Algorithm for Solving Linear Parabolic Evolution Equations ⋮ Wavelet-In-Time Multigrid-In-Space Preconditioning of Parabolic Evolution Equations ⋮ The Auxiliary Space Preconditioner for the de Rham Complex ⋮ Multiscale and high-dimensional problems. Abstracts from the workshop held July 28 -- August 3, 2013. ⋮ Time-multipatch discontinuous Galerkin space-time isogeometric analysis of parabolic evolution problems ⋮ A Well-Posed First Order System Least Squares Formulation of the Instationary Stokes Equations ⋮ Multilevel preconditioning and low-rank tensor iteration for space-time simultaneous discretizations of parabolic PDEs ⋮ Exponential convergence of hp-time-stepping in space-time discretizations of parabolic PDES ⋮ Low-rank tensor methods for partial differential equations ⋮ A space-time variational method for optimal control problems: well-posedness, stability and numerical solution ⋮ Space-time finite element methods stabilized using bubble function spaces ⋮ An Entropy Structure Preserving Space-Time Formulation for Cross-Diffusion Systems: Analysis and Galerkin Discretization ⋮ Space-Time Virtual Elements for the Heat Equation ⋮ Improved rates for a space-time FOSLS of parabolic PDEs ⋮ A space-time adaptive low-rank method for high-dimensional parabolic partial differential equations ⋮ Computation and learning in high dimensions. Abstracts from the workshop held August 1--7, 2021 (hybrid meeting) ⋮ Space-time methods for time-dependent partial differential equations. Abstracts from the workshop held February 6--12, 2022 ⋮ Numerical null controllability of the 1D linear Schrödinger equation ⋮ Space-time discretization of the heat equation ⋮ Numerical solution of parabolic problems based on a weak space-time formulation ⋮ Minimal residual space-time discretizations of parabolic equations: asymmetric spatial operators ⋮ Bi-parametric operator preconditioning ⋮ Coercive space-time finite element methods for initial boundary value problems ⋮ The $L^2$-Projection and Quasi-Optimality of Galerkin Methods for Parabolic Equations ⋮ Space-time least-squares finite elements for parabolic equations ⋮ An efficient space-time adaptive wavelet Galerkin method for time-periodic parabolic partial differential equations ⋮ The Ritz method for boundary problems with essential conditions as constraints ⋮ An exact realization of a modified Hilbert transformation for space-time methods for parabolic evolution equations ⋮ Space-time isogeometric analysis of parabolic evolution problems ⋮ Solving one-dimensional advection diffusion transport equation by using CDV wavelet basis ⋮ Low-rank approximation of linear parabolic equations by space-time tensor Galerkin methods ⋮ Space-Time Multipatch Discontinuous Galerkin Isogeometric Analysis for Parabolic Evolution Problems ⋮ Efficient Direct Space-Time Finite Element Solvers for Parabolic Initial-Boundary Value Problems in Anisotropic Sobolev Spaces ⋮ Further results on a space-time FOSLS formulation of parabolic PDEs ⋮ Efficient numerical approximation of a non-regular Fokker-Planck equation associated with first-passage time distributions ⋮ Optimal Local Approximation Spaces for Parabolic Problems ⋮ An ultraweak space-time variational formulation for the wave equation: Analysis and efficient numerical solution ⋮ Accuracy controlled data assimilation for parabolic problems ⋮ On long time integration of the heat equation
This page was built for publication: Stability of sparse space-time finite element discretizations of linear parabolic evolution equations
