Further results on a space-time FOSLS formulation of parabolic PDEs
Gregor Gantner, Rob Stevenson
Abstract
In [2019, Space-time least-squares finite elements for parabolic equations, arXiv:1911.01942 ] by Führer and 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.
Topics & Concepts
MathematicsParabolic partial differential equationFinite element methodLeast-squares function approximationEstimatorHeat equationConvergence (economics)Applied mathematicsMathematical analysisSpace (punctuation)Boundary (topology)SpacetimeSpace timePartial differential equationComputer sciencePhysicsEngineeringStatisticsChemical engineeringEconomic growthQuantum mechanicsOperating systemEconomicsThermodynamicsAdvanced Numerical Methods in Computational MathematicsAdvanced Mathematical Modeling in EngineeringNumerical methods in inverse problems