Graded mesh approximation in weighted Sobolev spaces and elliptic equations in 2D
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Publication:5264125
DOI10.1090/S0025-5718-2015-02934-2zbMath1319.65109OpenAlexW2066322206MaRDI QIDQ5264125
Publication date: 20 July 2015
Published in: Mathematics of Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0025-5718-2015-02934-2
convergenceSobolev spaceerror estimatesfinite elementssingularitiesgraded meshesstrongly elliptic interface/boundary value problems
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) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)
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Cites Work
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- Meshfree particle methods for thin plates
- A posteriori error estimation of hierarchical type for the Schrödinger operator with inverse square potential
- \(C^0\) interior penalty methods for fourth order elliptic boundary value problems on polygonal domains
- Analysis of the finite element method for transmission/mixed boundary value problems on general polygonal domains
- Finite element analysis for the axisymmetric Laplace operator on polygonal domains
- A finite element method for interface problems in domains with smooth boundaries and interfaces
- A family of non-conforming elements and the analysis of Nitsche's method for a singularly perturbed fourth order problem
- On the accuracy of least squares methods in the presence of corner singularities
- Well-posedness of the fundamental boundary value problems for constrained anisotropic elastic materials
- Direct and inverse error estimates for finite elements with mesh refinements
- Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
- On the finite element method for the biharmonic Dirichlet problem in polygonal domains; quasi-optimal rate of convergence
- Finite element method for domains with corners
- Improving the rate of convergence of `high order finite elements' on polygons and domains with cusps
- Multigrid methods for the symmetric interior penalty method on graded meshes
- A $\mathcal{C}^0$ Interior Penalty Method for a Fourth Order Elliptic Singular Perturbation Problem
- A Coarsening Algorithm on Adaptive Grids by Newest Vertex Bisection and Its Applications
- Regularity of the solutions for elliptic problems on nonsmooth domains in ℝ3, Part I: countably normed spaces on polyhedral domains
- Finite element exterior calculus, homological techniques, and applications
- Finite element exterior calculus: from Hodge theory to numerical stability
- Uniform convergence of the multigrid V‐cycle on graded meshes for corner singularities
- Weighted-Norm First-Order System Least-Squares (FOSLS) for Div/Curl Systems with Three Dimensional Edge Singularities
- Conform and mixed finite element schemes for the Dirichlet problem for the Bilaplacian in plane domains with corners
- First-Order System Least Squares for Second-Order Partial Differential Equations: Part I
- Regularity estimates for elliptic boundary value problems in Besov spaces
- Regularity estimates for elliptic boundary value problems with smooth data on polygonal domains
- Multigrid Methods for Anisotropic Edge Refinement
- EXPONENTIAL CONVERGENCE OF hp-FEM FOR MAXWELL EQUATIONS WITH WEIGHTED REGULARIZATION IN POLYGONAL DOMAINS
- Weighted‐Norm First‐Order System Least Squares (FOSLS) for Problems with Corner Singularities
- Least Squares Methods for 2mth Order Elliptic Boundary-Value Problems
- Analysis of First-Order System Least Squares (FOSLS) for Elliptic Problems with Discontinuous Coefficients: Part I
