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Anisotropic interpolation error estimates using a new geometric parameter
We present precise anisotropic interpolation error estimates for smooth functions using a new geometric parameter and derive inverse inequalities on...
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Anisotropic Raviart–Thomas interpolation error estimates using a new geometric parameter
We present precise Raviart–Thomas interpolation error estimates on anisotropic meshes. The novel aspect of our theory is the introduction of a new...
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Interpolation Error Estimates for Two Dimensions
We formulate the fundamental theoretical results which are later employed for the anisotropic mesh adaptation method. First, we recall the geometry...
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Interpolation Error Estimates for Three Dimensions
We extend the theoretical results to the three-dimensional case. In the same spirit as for the two-dimensional case, we recall the geometry of a...
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Ritz-type projectors with boundary interpolation properties and explicit spline error estimates
In this paper we construct Ritz-type projectors with boundary interpolation properties in finite dimensional subspaces of the usual Sobolev space and...
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Pointwise Error Estimates of Numerical Solutions to Linear Quadratic Optimal Control Problems
An auxiliary optimal control problem is formulated that provides with its unique solution, a continuous representation of the global error of a...
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Error-constant estimation under the maximum norm for linear Lagrange interpolation
For the linear Lagrange interpolation over a triangular domain, we propose an efficient algorithm to rigorously evaluate the interpolation error...
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Estimates of Solutions to Infinite Systems of Linear Equations and the Problem of Interpolation by Cubic Splines on the Real Line
We study the solvability of bi-infinite systems of linear equations whose matrices are diagonally dominant. We prove that the estimates of the...
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Optimal Error Estimates for Chebyshev Approximations of Functions with Endpoint Singularities in Fractional Spaces
In this paper, we introduce some new definitions and more general results of fractional spaces in order to deal with functions with endpoint...
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Optimal error estimates for non-conforming approximations of linear parabolic problems with minimal regularity
We consider a general linear parabolic problem with extended time boundary conditions (including initial value problems and periodic ones), and...
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Error Estimates of EDG-HDG Methods for the Stokes Equations with Dirac Measures
In this paper, we analyze the hybridized, embedded-hybridized and embedded discontinuous Galerkin methods for the Stokes equations with Dirac...
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A New A Posteriori Error Estimates for Optimal Control Problems Governed by Parabolic Integro-Differential Equations
AbstractIn this paper, we provide a new a posteriori error analysis for linear finite element approximation of a parabolic integro-differential...
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Error Estimates of hp Spectral Element Methods in Nonlinear Optimal Control Problem
The main purpose of this paper is to discuss hp spectral element method for optimal control problem governed by a nonlinear elliptic equation with
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Pointwise error estimates for linear finite element approximation to elliptic Dirichlet problems in smooth domains
In this paper, we consider pointwise error estimation for the linear finite element approximation to −Δ u + u = f in Ω, u = g on Γ, where Ω is a...
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Error Estimates for Fractional Semilinear Optimal Control on Lipschitz Polytopes
We adopt the integral definition of the fractional Laplace operator and analyze solution techniques for fractional, semilinear, and elliptic optimal...
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Interpolation operators for parabolic problems
We introduce interpolation operators with approximation and stability properties suited for parabolic problems in primal and mixed formulations. We...
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An Anisotropic hp-mesh Adaptation Method for Time-Dependent Problems Based on Interpolation Error Control
We propose an efficient mesh adaptive method for the numerical solution of time-dependent partial differential equations considered in the fixed...
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On the Optimal Interpolation of Functions
AbstractThe construction of optimal interpolation formulas is discussed. First, an exact upper bound for the error of an interpolation formula in the...
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Error Estimates for Adaptive Spectral Decompositions
Adaptive spectral (AS) decompositions associated with a piecewise constant function, u , yield small subspaces where the characteristic functions...
