Stability of Galerkin discretizations of a mixed space–time variational formulation of parabolic evolution equations
Rob Stevenson, Jan Westerdiep
Abstract
Abstract We analyze Galerkin discretizations of a new well-posed mixed space–time variational formulation of parabolic partial differential equations. For suitable pairs of finite element trial spaces, the resulting Galerkin operators are shown to be uniformly stable. The method is compared to two related space–time discretization methods introduced by Andreev (2013, Stability of sparse space-time finite element discretizations of linear parabolic evolution equations. IMA J. Numer. Anal., 33, 242–260) and by Steinbach (2015, Space-time finite element methods for parabolic problems. Comput. Methods Appl. Math., 15, 551–566).
Topics & Concepts
MathematicsDiscretizationGalerkin methodFinite element methodParabolic partial differential equationDiscontinuous Galerkin methodPartial differential equationMathematical analysisSpace (punctuation)Stability (learning theory)Applied mathematicsPhysicsLinguisticsComputer scienceMachine learningThermodynamicsPhilosophyAdvanced Numerical Methods in Computational MathematicsAdvanced Mathematical Modeling in EngineeringAdvanced Numerical Analysis Techniques