A Local Space-Time Adaptive Scheme in Solving Two-Dimensional Parabolic Problems Based on Domain Decomposition Methods
Copyright policy )A Local Space-Time Adaptive Scheme in Solving Two-Dimensional Parabolic Problems Based on Domain Decomposition Methods
Summary: We describe a local space-time adaptive refinement and derefinement method for solving systems of parabolic partial differential equations. Solutions are calculated on local space-time meshes using a domain decomposition finite element algorithm in space and an extrapolation algorithm in time. An a posteriori spatial error estimate controls a local spatial refinement strategy and an a posteriori temporal error estimate monitors temporal refinement and order of the integration. A multiplicative Schwarz algorithm is used to coordinate solutions between overlapping grids. We use nearly minimal fine meshes which follow the dynamics of the problems in an efficient manner.
domain decomposition, Error bounds for initial value and initial-boundary value problems involving PDEs, extrapolation methods, Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs, finite element, Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs, Nonlinear parabolic equations, adaptive mesh refinement, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, error estimate, multiplicative Schwarz algorithm
domain decomposition, Error bounds for initial value and initial-boundary value problems involving PDEs, extrapolation methods, Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs, finite element, Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs, Nonlinear parabolic equations, adaptive mesh refinement, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, error estimate, multiplicative Schwarz algorithm
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