Nonconforming least-squares method for elliptic partial differential equations with smooth interfaces

DOI10.1007/s10915-011-9572-5zbMath1272.65093OpenAlexW1970774037MaRDI QIDQ357812

N. Kishore Kumar, G. Naga Raju

Publication date: 13 August 2013

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-011-9572-5

zbMATH Keywords

stabilityspectral element methodconjugate gradient methoderror estimateleast-squarespreconditionerexponential convergencenonconformingelliptic interface problems

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Preconditioners for iterative methods (65F08)

Related Items (6)

Spectral element method for elliptic equations with periodic boundary conditions ⋮ Nonconforming spectral element method: a friendly introduction in one dimension and a short review in higher dimensions ⋮ Spectral element method for parabolic interface problems ⋮ Fully discrete least-squares spectral element method for parabolic interface problems ⋮ A study of spectral element method for elliptic interface problems with nonsmooth solutions in $\mathbb{R}^{2}$ ⋮ Spectral element method for three dimensional elliptic problems with smooth interfaces

Uses Software

• IIMPACK

Cites Work

• Unnamed Item
• A finite element method for interface problems in domains with smooth boundaries and interfaces
• \(h\)-\(p\) spectral element method for elliptic problems on nonsmooth domains using parallel computers
• Least-squares finite element methods
• Optimal a priori estimates for higher order finite elements for elliptic interface problems
• Least-squares hp/spectral element method for elliptic problems
• New Cartesian grid methods for interface problems using the finite element formulation
• Analysis of a discontinuous least squares spectral element method
• Mortar finite elements for interface problems
• Nonconforming \(h\)-\(p\) spectral element methods for elliptic problems
• Preconditioners for spectral element methods for elliptic and parabolic problems
• \(hp\)-adaptive least squares spectral element method for hyperbolic partial differential equations
• The finite element method for elliptic equations with discontinuous coefficients
• Transfinite element methods: Blending-function interpolation over arbitrary curved element domains
• A discontinuous Galerkin method for elliptic interface problems with application to electroporation
• Immersed-Interface Finite-Element Methods for Elliptic Interface Problems with Nonhomogeneous Jump Conditions
• Fitted and Unfitted Finite-Element Methods for Elliptic Equations with Smooth Interfaces
• The $h{\text{ - }}p$ Version of the Finite Element Method for Domains with Curved Boundaries
• On the poisson equation with intersecting interfaces
• The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
• Least-Squares Finite Element Approximations to Solutions of Interface Problems
• A mortar element method for elliptic problems with discontinuous coefficients
• An Unfitted Discontinuous Galerkin Method Applied to Elliptic Interface Problems
• The Explicit-Jump Immersed Interface Method: Finite Difference Methods for PDEs with Piecewise Smooth Solutions
• Nonconforming spectral/hp element methods for elliptic systems
• The Immersed Interface Method
• Analysis of First-Order System Least Squares (FOSLS) for Elliptic Problems with Discontinuous Coefficients: Part I
• Analysis of First-Order System Least Squares (FOSLS) for Elliptic Problems with Discontinuous Coefficients: Part II

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