Further results on a space-time FOSLS formulation of parabolic PDEs
arXiv:2005.11000 · doi:10.1051/m2an/2020084
Abstract
In [2019, Space-time least-squares finite elements for parabolic equations, arXiv:1911.01942] by Führer& Karkulik, well-posedness of a space-time First-Order System Least-Squares formulation of the heat equation was proven. In the present work, this result is generalized to general second order parabolic PDEs with possibly inhomogenoeus boundary conditions, and plain convergence of a standard adaptive finite element method driven by the least-squares estimator is demonstrated. The proof of the latter easily extends to a large class of least-squares formulations.
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Cited by in corpus (13)
- A wavelet-in-time, finite element-in-space adaptive method for parabolic evolution equations
- A short note on plain convergence of adaptive least-squares finite element methods
- Applications of a space-time FOSLS formulation for parabolic PDEs
- Improved rates for a space-time FOSLS of parabolic PDEs
- Plain convergence of adaptive algorithms without exploiting reliability and efficiency
- A well-posed First Order System Least Squares formulation of the instationary Stokes equations
- Space-time virtual elements for the heat equation
- Accuracy controlled data assimilation for parabolic problems
- Design and performance of a space-time virtual element method for the heat equation on prismatic meshes
- An adaptive space-time method for nonlinear poroviscoelastic flows with discontinuous porosities
- Space-time FEM-BEM couplings for parabolic transmission problems
- Fluid flow channeling and mass transport with discontinuous porosity distribution
- Aubin--Nitsche-type estimates for space-time FOSLS for parabolic PDEs