Simultaneous Approximation in Scales of Banach Spaces

DOI10.2307/2006327zbMath0404.41005OpenAlexW4241571195MaRDI QIDQ4189603

James H. Bramble, L. Ridgway Scott

Publication date: 1978

Full work available at URL: https://doi.org/10.2307/2006327

zbMATH Keywords

Banach SpacesSimultaneous ApproximationOptimal ApproximationInterpolation MethodTheory of Finite Element Methods

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Multidimensional problems (41A63) Rate of convergence, degree of approximation (41A25) Spline approximation (41A15)

Related Items (25)

Local convergence of the boundary element method on polyhedral domains ⋮ Error and stability estimates of a least-squares variational kernel-based method for second order elliptic PDEs ⋮ A mixed-Lagrange multiplier finite element method for the polyharmonic equation ⋮ An analysis of discretizations of the Helmholtz equation in \(L^2\) and in negative norms ⋮ Interior error estimates of the Ritz method for pseudo-differential equations ⋮ Abstract estimates of the rate of convergence for optimal control problems ⋮ Runge-Kutta approximation for \(C_0\)-semigroups in the graph norm with applications to time domain boundary integral equations ⋮ Galerkin approximation with quadrature for the screen problem in \(\mathbb{R}^3\) ⋮ Simultaneous quasi‐optimal convergence rates in FEM‐BEM coupling ⋮ A least-squares approach based on a discrete minus one inner product for first order systems ⋮ General DG-methods for highly indefinite Helmholtz problems ⋮ New Mixed Elements for Maxwell Equations ⋮ On superconvergence of Runge-Kutta convolution quadrature for the wave equation ⋮ Two mixed finite element methods for the simply supported plate problem ⋮ Error estimates for the numerical approximation of Neumann control problems governed by a class of quasilinear elliptic equations ⋮ An Error Estimate of the Least Squares Finite Element Method for the Stokes Problem in Three Dimensions ⋮ On the boundary element method with mesh refinement on curves with corners ⋮ An Iterative Finite Element Method for Approximating the Biharmonic Equation ⋮ $L_\infty $-convergence of finite element Galerkin approximations for parabolic problems ⋮ Second Order Estimates in Interpolation Theory and Applications ⋮ Least-squares methods for Stokes equations based on a discrete minus one inner product ⋮ A least-squares finite element method for incompressible flow in stress-velocity-pressure version ⋮ Convergence Rates for Tikhonov Regularization in Finite-Dimensional Subspaces of Hilbert Scales ⋮ Galerkin methods with splines for singular integral equations over (0,1) ⋮ Simultaneous approximation in negative norms of arbitrary order

Cites Work

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• Discrete time Galerkin methods for a parabolic boundary value problem
• Galerkin methods for parabolic equations with nonlinear boundary conditions
• Simplified Proofs of Error Estimates for the Least Squares Method for Dirichlet's Problem
• Interior Estimates for Ritz-Galerkin Methods
• The Finite Element Method with Penalty
• Nonuniform Error Estimates for the Finite Element Method
• The finite element method for ill-posed problems
• $L^2 $ Error Bounds for the Rayleigh–Ritz–Galerkin Method
• Rayleigh‐Ritz‐Galerkin methods for dirichlet's problem using subspaces without boundary conditions
• Least Squares Methods for 2mth Order Elliptic Boundary-Value Problems

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