Spectral element methods for parabolic problems
Copyright policy )Spectral element methods for parabolic problems
A spectral element method for parabolic initial value problems on smooth domains using parallel computers is presented. The space domain is divided into a number of regular quadrilaterals of size \(h\) and the time step is proportional to \(h^2\). At each time step we minimize a least-squares functional in different Sobolev norms and a term which measures the jump in the function and its derivatives across the inter-element boundaries. The Sobolev spaces used are of different order in space and time. A preconditioner for the minimization problem is defined which allows the problem to decouple. Error estimates are obtained for both the \(h\) and \(p\) versions of the method.
Least-squares method, Applied Mathematics, Parallel numerical computation, Parallel preconditioners, domain decomposition, Computational Mathematics, Error bounds for initial value and initial-boundary value problems involving PDEs, Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs, error estimates, Sobolev spaces of different orders in space and time, Domain decomposition, Initial value problems for second-order parabolic equations, spectral elements, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, parabolic problems, least-squares, parallel preconditioners, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
Least-squares method, Applied Mathematics, Parallel numerical computation, Parallel preconditioners, domain decomposition, Computational Mathematics, Error bounds for initial value and initial-boundary value problems involving PDEs, Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs, error estimates, Sobolev spaces of different orders in space and time, Domain decomposition, Initial value problems for second-order parabolic equations, spectral elements, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, parabolic problems, least-squares, parallel preconditioners, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
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