Analysis of finite element methods for second order boundary value problems using mesh dependent norms

DOI10.1007/BF01463997zbMath0404.65055OpenAlexW1985787639MaRDI QIDQ1256841

John E. Osborn, Ivo M. Babuška

Publication date: 1980

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/132658

zbMATH Keywords

StabilityApproximationRitz-GalerkinBoundary Value ProblemsApproximate SolutionAnalysis of Finite Element MethodsL2-Space-Norm EstimatesNew ApproachPartial Differential Equations of Elliptic TypeSobolev Norm Estimates

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) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

Related Items (25)

An analysis of viscous splitting and adaptivity for steady-state convection-diffusion problems ⋮ Quasi-optimality of adaptive finite element methods for controlling local energy errors ⋮ Convergence of a continuous Galerkin method with mesh modification for nonlinear wave equations ⋮ On the Babuška-Osborn approach to finite element analysis: \(L^2\) estimates for unstructured meshes ⋮ Regularity estimates and optimal finite element methods in \(W_p^1\) on polygonal domains ⋮ Discontinuous Galerkin Methods for Ordinary Differential Equations ⋮ Convergence and quasi-optimality of an adaptive finite element method for controlling \(L_{2}\) errors ⋮ Characterization of the solvability of generalized constrained variational equations ⋮ Analysis of discontinuous Galerkin methods using mesh-dependent norms and applications to problems with rough data ⋮ Approximation of eigenvalues of differential equations with non-smooth coefficients ⋮ Galerkin schemes and inverse boundary value problems in reflexive Banach spaces ⋮ An analysis of a cell-vertex finite volume method for a parabolic convection-diffusion problem ⋮ Best approximation property in the $W^1_{\infty }$ norm for finite element methods on graded meshes ⋮ Finite element error analysis of a variational multiscale method for the Navier-Stokes equations ⋮ A space-time finite element method for the nonlinear Schrödinger equation: the discontinuous Galerkin method ⋮ On the numerical approximation of p‐biharmonic and ∞‐biharmonic functions ⋮ Robust localization of the best error with finite elements in the reaction-diffusion norm ⋮ The $W^1_p$ stability of the Ritz projection on graded meshes ⋮ Lower norm error estimates for approximate solutions of differential equations with non-smooth coefficients ⋮ An error analysis for the finite element method applied to convection diffusion problems ⋮ Finite element methods: Principles for their selection ⋮ Maximum-norm-stability and error-estimates in Galerkin methods for parabolic equations in one space variable ⋮ Singularities and treatments of elliptic boundary value problems. ⋮ Feedback and adaptive finite element solution of one-dimensional boundary value problems ⋮ Approximation of the solution of a fourth order boundary value problem with nonsmooth coefficient

Cites Work

• Ein Kriterium für die Quasi-Optimalität des Titzschen Verfahrens
• Error-bounds for finite element method
• A Weak Discrete Maximum Principle and Stability of the Finite Element Method in L ∞ on Plane Polygonal Domains. I
• Interior Estimates for Ritz-Galerkin Methods
• Optimal L ∞ Error Estimates for Galerkin Approximations to Solutions of Two-Point Boundary Value Problems
• Approximation of the Eigenvalues of a Nonselfadjoint Operator Arising in the Study of the Stability of Stationary Solutions of the Navier–Stokes Equations
• Uniform Convergence of Galerkin's Method for Splines on Highly Nonuniform Meshes
• An Optimal $L_\infty $ Error Estimate for Galerkin Approximations to Solutions of Two-Point Boundary Value Problems

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