The $L^2$-Projection and Quasi-Optimality of Galerkin Methods for Parabolic Equations

DOI10.1137/140996811zbMath1382.65328OpenAlexW2300734653MaRDI QIDQ2788624

Andreas Veeser, Francesca Tantardini

Publication date: 22 February 2016

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

Full work available at URL: https://doi.org/10.1137/140996811

zbMATH Keywords

finite element methodsGalerkin approximationsquasi-optimality\(L^2\)-projectionparabolic initial-boundary value problems

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) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (15)

Interpolation operator on negative Sobolev spaces ⋮ Quasi-Optimality Constants for Parabolic Galerkin Approximation in Space ⋮ Quasi-Optimal Nonconforming Methods for Symmetric Elliptic Problems. I---Abstract Theory ⋮ A pollution-free ultra-weak FOSLS discretization of the Helmholtz equation ⋮ Global and Interior Pointwise best Approximation Results for the Gradient of Galerkin Solutions for Parabolic Problems ⋮ Interpolation operators for parabolic problems ⋮ Guaranteed, Locally Space-Time Efficient, and Polynomial-Degree Robust a Posteriori Error Estimates for High-Order Discretizations of Parabolic Problems ⋮ Asymptotically Constant-Free and Polynomial-Degree-Robust a Posteriori Estimates for Space Discretizations of the Wave Equation ⋮ Minimal residual methods in negative or fractional Sobolev norms ⋮ A space-time adaptive low-rank method for high-dimensional parabolic partial differential equations ⋮ Time-Parallel Iterative Solvers for Parabolic Evolution Equations ⋮ On the Sobolev and $L^p$-Stability of the $L^2$-Projection ⋮ Space-time least-squares finite elements for parabolic equations ⋮ Quasi-best approximation in optimization with PDE constraints ⋮ Low-rank approximation of linear parabolic equations by space-time tensor Galerkin methods

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