\(h\)-\(p\) spectral element method for elliptic problems on nonsmooth domains using parallel computers

DOI10.1007/s00607-006-0176-0zbMath1109.65105OpenAlexW2100055794MaRDI QIDQ854702

Satyendra Tomar

Publication date: 6 December 2006

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00607-006-0176-0

zbMATH Keywords

algorithmstabilitynumerical resultsleast-squares methodspectral element methodSchur complementDirichlet problemsparallel computationconjugate gradient methodcorner singularitiesPoisson equationelliptic boundary value problemsexponential accuracyalmost optimal preconditionerleast-squares collocation method

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Complexity and performance of numerical algorithms (65Y20)

Related Items (21)

Spectral element method for elliptic equations with periodic boundary conditions ⋮ Nonconforming least-squares method for elliptic partial differential equations with smooth interfaces ⋮ Nonconforming spectral element method: a friendly introduction in one dimension and a short review in higher dimensions ⋮ Exponentially accurate nonconforming least-squares spectral element method for elliptic problems on unbounded domain ⋮ Spectral element method for parabolic initial value problem with non-smooth data: analysis and application ⋮ Least-squares spectral element preconditioners for fourth order elliptic problems ⋮ Exponentially accurate spectral element method for fourth order elliptic problems ⋮ Least squares \(h\)-\(p\) spectral element method for elliptic eigenvalue problems ⋮ \(h\)-\(p\) spectral element methods for three dimensional elliptic problems on non-smooth domains ⋮ Spectral element method for parabolic interface problems ⋮ Fully discrete least-squares spectral element method for parabolic interface problems ⋮ Preconditioners for spectral element methods for elliptic and parabolic problems ⋮ Nonconforming least-squares spectral element method for European options ⋮ \(h\)-\(p\) spectral element methods for three dimensional elliptic problems on non-smooth domains. III: Error estimates, preconditioners, computational techniques and numerical results ⋮ Least-squares hp/spectral element method for elliptic problems ⋮ Nonconforming spectral/hp element methods for elliptic systems ⋮ A study of spectral element method for elliptic interface problems with nonsmooth solutions in $\mathbb{R}^{2}$ ⋮ Spectral method and spectral element method for three dimensional linear elliptic system: analysis and application ⋮ Spectral element method for three dimensional elliptic problems with smooth interfaces ⋮ Least-squares spectral element method for three dimensional Stokes equations ⋮ \(h\)-\(p\) spectral element methods for three dimensional elliptic problems on non-smooth domains. I: Regularity estimates and stability theorem

Cites Work

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