\(h\)-\(p\) spectral element methods for three dimensional elliptic problems on non-smooth domains. II: Proof of stability theorem

DOI10.1007/s12044-015-0239-2zbMath1403.65153OpenAlexW2166023505MaRDI QIDQ746363

D. Kharzeev

Publication date: 16 October 2015

Published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12044-015-0239-2

zbMATH Keywords

spectral element methodstability estimategeometric meshedge singularitymodified coordinatesvertex singularityvertex-edge singularityquasi uniform mesh

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Boundary value problems for second-order elliptic equations (35J25) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12)

Related Items

Exponential convergence of \(hp\)-FEM for elliptic problems in polyhedra: mixed boundary conditions and anisotropic polynomial degrees, Nonconforming spectral element method: a friendly introduction in one dimension and a short review in higher dimensions, \(h\)-\(p\) spectral element methods for three dimensional elliptic problems on non-smooth domains. III: Error estimates, preconditioners, computational techniques and numerical results, \(h\)-\(p\) spectral element methods for three dimensional elliptic problems on non-smooth domains. I: Regularity estimates and stability theorem

Cites Work

• \(h\)-\(p\) spectral element methods for three dimensional elliptic problems on non-smooth domains
• Approximation properties of the \(h\)-\(p\) version of the finite element method
• Stability estimates for h-p spectral element methods for general elliptic problems on curvilinear domains
• \(h\)-\(p\) spectral element methods for three dimensional elliptic problems on non-smooth domains. I: Regularity estimates and stability theorem
• Finite element method for solving problems with singular solutions
• Regularity of the solutions for elliptic problems on nonsmooth domains in ℝ³, Part I: countably normed spaces on polyhedral domains
• Regularity of the solutions for elliptic problems on nonsmooth domains in ℝ³. Part II: Regularity in neighbourhoods of edges
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