On the Error Estimation of the Finite Element Method for the Boundary Value Problems with Singularity in the Lebesgue Weighted Space

DOI10.1080/01630563.2013.809582zbMath1286.65146OpenAlexW2084719427MaRDI QIDQ5396934

H. I. Rukavishnikova, Victor Anatolievich Rukavishnikov

Publication date: 4 February 2014

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630563.2013.809582

zbMATH Keywords

stabilityconvergencefinite element methodweighted Sobolev spacesdegenerationnumerical experimentelliptic problem with nonnegative formR-\(\nu\)-generalized solutions

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Degenerate elliptic equations (35J70)

Related Items (12)

Dirichlet problem with degeneration of the input data on the boundary of the domain ⋮ Weighted FEM for Two-Dimensional Elasticity Problem with Corner Singularity ⋮ The Finite Difference Method for Boundary Value Problem with Singularity ⋮ Weighted finite element method and body of optimal parameters for elasticity problem with singularity ⋮ On the existence and uniqueness of \(R_v\)-generalized solution for Dirichlet problem with singularity on all boundary ⋮ On the isomorphic mapping of weighted spaces by an elliptic operator with degeneration on the domain boundary ⋮ On the existence and uniqueness of an \(R_\nu\)-generalized solution of a boundary value problem with uncoordinated degeneration of the input data ⋮ Unnamed Item ⋮ Weighted finite element method for the Stokes problem with corner singularity ⋮ New Approximate Method for Solving the Stokes Problem in a Domain with Corner Singularity ⋮ Existence and uniqueness of an \(R_ \nu\)-generalized solution of the Dirichlet problem for the Lamé system with a corner singularity ⋮ New numerical method for the rotation form of the Oseen problem with corner singularity

Cites Work

• Unnamed Item
• Weighted finite element method for an elasticity problem with singularity
• New numerical method for solving time-harmonic Maxwell equations with strong singularity
• The \(R_\nu \)-generalized solution of a boundary value problem with a singularity belongs to the space \(W_{2,\nu +\beta /2+\kappa +1}^{\kappa +2} (\Omega , \delta )\)
• The finite element method for a boundary value problem with strong singularity
• Numerical solution to the time-dependent Maxwell equations in two-dimensional singular domains: The singular complement method
• Weighted edge finite element method for Maxwell's equations with strong singularity
• Coercive estimate for a boundary value problem with noncoordinated degeneration of the data
• On the coercivity of the \(R_{v}\)-generalized solution of the first boundary value problem with coordinated degeneration of the input data
• Analysis of a modified Schrödinger operator in 2D: Regularity, index, and FEM
• Ein Kriterium für die Quasi-Optimalität des Titzschen Verfahrens
• A finite element method scheme for boundary value problems with noncoordinated degeneration of input data
• On the finite element method for elliptic problems with degenerate and singular coefficients
• EXPONENTIAL CONVERGENCE OF hp-FEM FOR MAXWELL EQUATIONS WITH WEIGHTED REGULARIZATION IN POLYGONAL DOMAINS

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