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Enhanced Error Estimates for Augmented Subspace Method
In this paper, some enhanced error estimates are derived for the augmented subspace methods which are designed for solving eigenvalue problems. For...
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Unconditionally superconvergent error estimates of a linearized Galerkin finite element method for the nonlinear thermistor problem
In this paper, a linearized Galerkin fully-discrete scheme is proposed and investigated for the time-dependent nonlinear thermistor problem, where...
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Stability and Error Estimates of High Order BDF-LDG Discretizations for the Allen–Cahn Equation
AbstractWe construct high order local discontinuous Galerkin (LDG) discretizations coupled with third and fourth order backward differentiation...
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Error Estimates in Polygonal Domains
Consider the second-order elliptic equations with mixed boundary conditions in a polygonal domain. This chapter is concerned with the regularity...
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Lagrange Finite Elements and Interpolation
The aim of this chapter is to give a brief introduction to finite element spaces, and introduce some useful interpolation estimates in fractional...
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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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Error Estimates of Finite Element Method for the Incompressible Ferrohydrodynamics Equations
In this paper, we consider the Shliomis ferrofluid model and study its numerical approximation. We investigate a first-order energy-stable fully...
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A posteriori error estimates for a dual finite element method for singularly perturbed reaction–diffusion problems
A posteriori error estimates are established for a two-step dual finite element method for singularly perturbed reaction–diffusion problems. The...
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A posteriori error estimates for the time-dependent Navier-Stokes system coupled with the convection-diffusion-reaction equation
In this paper we study the a posteriori error estimates for the time dependent Navier-Stokes system coupled with the convection-diffusion-reaction...
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Convergence Estimates for Stationary Radial Basis Function Interpolation and for Semi-discrete Collocation-Schemes
We give a Fourier-theoretic analysis of the convergence of semi-discrete Radial Basis Function interpolation on regular grids and of the associated...
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Nonsmooth data optimal error estimates by energy arguments for subdiffusion equations with memory
This paper considers the semidiscrete Galerkin finite element approximation for time fractional diffusion equations with memory in a bounded convex...
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Error estimates for total-variation regularized minimization problems with singular dual solutions
Recent quasi-optimal error estimates for the finite element approximation of total-variation regularized minimization problems using the...
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General theory of interpolation error estimates on anisotropic meshes
We propose a general theory of estimating interpolation error for smooth functions in two and three dimensions. In our theory, the error of...
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Asymptotically exact a posteriori error estimates for the BDM finite element approximation of mixed Laplace eigenvalue problems
We derive optimal and asymptotically exact a posteriori error estimates for the approximation of the eigenfunction of the Laplace eigenvalue problem....
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A Posteriori Error Estimates and Adaptive Error Control for Permittivity Reconstruction in Conductive Media
An inverse problem of reconstruction of the spatially distributed dielectric permittivity function in the Maxwell’s system is considered. The...
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Root Mean Square Error Estimates for the Projection-Difference Method for the Approximate Solution of a Parabolic Equation with a Periodic Condition for the Solution
Using the projection-difference method, we construct an approximate solution of an abstract linear parabolic equation in a separable Hilbert space...
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Error estimates for POD-DL-ROMs: a deep learning framework for reduced order modeling of nonlinear parametrized PDEs enhanced by proper orthogonal decomposition
POD-DL-ROMs have been recently proposed as an extremely versatile strategy to build accurate and reliable reduced order models (ROMs) for nonlinear...
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Two-Dimensional Interpolation of Functions by Cubic Splines in the Presence of Boundary Layers
We study interpolation of a function of two variables with large gradients in regions of a boundary layer under the assumption that the Shishkin...