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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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Estimation of Pointwise Approximation Error Using a Set of Numerical Solutions
AbstractThis paper deals with estimation of local (pointwise) approximation error on an ensemble of numerical solutions obtained by using independent...
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Sharp error estimate of Grünwald-Letnikov scheme for a multi-term time fractional diffusion equation
The sharp pointwise-in-time error estimate of the Grünwald-Letnikov scheme for the initial-boundary value problem of a multi-term time fractional...
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Pointwise-in-time error estimate of an ADI scheme for two-dimensional multi-term subdiffusion equation
We use alternating direction implicit (ADI) difference method to solve a two-dimensional multi-term time-fractional subdiffusion 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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On pointwise error estimates for Voronoï-based finite volume methods for the Poisson equation on the sphere
In this paper, we give pointwise estimates of a Voronoï-based finite volume approximation of the Laplace-Beltrami operator on Voronoï-Delaunay...
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Pointwise error estimate in difference setting for the two-dimensional nonlinear fractional complex Ginzburg-Landau equation
In this paper, we propose a three-level linearized implicit difference scheme for the two-dimensional spatial fractional nonlinear complex...
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Local pointwise convergence of the 3D finite element
For an elliptic problem with variable coefficients in three dimensions, this article discusses local pointwise convergence of the three-dimensional...
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Asymptotic pointwise error estimates for reconstructing shift-invariant signals with generators in a hybrid-norm space
Sampling and reconstruction of signals in a shift-invariant space are generally studied under the requirement that the generator is in a stronger...
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Optimal Balanced-Norm Error Estimate of the LDG Method for Reaction–Diffusion Problems I: The One-Dimensional Case
A singularly perturbed reaction–diffusion problem in 1D is solved numerically by a local discontinuous Galerkin (LDG) finite element method. For this...
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A Novel Discrete Fractional Grönwall-Type Inequality and Its Application in Pointwise-in-Time Error Estimates
We present a family of fully-discrete schemes for numerically solving nonlinear sub-diffusion equations, taking the weak regularity of the exact...
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Pointwise and weighted estimates for Bernstein-Kantorovich type operators including beta function
We establish a Kantorovich variant of Bernstein operators including the beta function inspired by the King-type operators which preserve certain...
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Pointwise a Posteriori Error Analysis of a Finite Element Method for the Signorini Problem
In this article, we develop a posteriori error control of conforming finite element method in maximum norm for the one-body contact problem. The...
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Pointwise Estimation of Sign-Preserving Polynomial Approximations on Arcs in the Complex Plane
In 2014, V. Andrievskii proved that if a real-valued function f ∈ Lip 𝛼 , 0 < 𝛼 < 1 , defined on a given smooth Jordan curve satisfying the Dini...
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Pointwise adaptive non-conforming finite element method for the obstacle problem
In this article, we develop a posteriori error analysis of a non-conforming finite element method in the supremum norm for the elliptic obstacle...
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Weak-Type (1,1) Inequality for Discrete Maximal Functions and Pointwise Ergodic Theorems Along Thin Arithmetic Sets
We establish weak-type (1, 1) bounds for the maximal function associated with ergodic averaging operators modeled on a wide class of thin...
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Analysis and Discretization for an Optimal Control Problem of a Variable-Coefficient Riesz-Fractional Diffusion Equation with Pointwise Control Constraints
We present a mathematical and numerical study for a pointwise optimal control problem governed by a variable-coefficient Riesz-fractional diffusion...
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Derivation of a Kalman-type filter for linear systems with pointwise delay in signal noise
Recently, it was demonstrated that a modification of the Kalman-filtering model with a pointwise delay of the signal noise could improve...
