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Error Bounds for Discrete-Continuous Free Flight Trajectory Optimization
Two-stage methods addressing continuous shortest path problems start local minimization from discrete shortest paths in a spatial graph. The...
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A Posteriori Error Estimates for Elliptic Eigenvalue Problems Using Auxiliary Subspace Techniques
We propose an a posteriori error estimator for high-order p - or hp -finite element discretizations of selfadjoint linear elliptic eigenvalue problems...
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Error estimates of finite volume method for Stokes optimal control problem
In this paper, we discuss a priori error estimates for the finite volume element approximation of optimal control problem governed by Stokes...
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A Posteriori Error Estimates for Parabolic Optimal Control Problems with Controls Acting on Lower Dimensional Manifolds
This article concerns a posteriori error estimates for the fully discrete finite element approximation to the optimal control problem governed by...
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Weighted Error Estimates for Transient Transport Problems Discretized Using Continuous Finite Elements with Interior Penalty Stabilization on the Gradient Jumps
In this paper we consider the semi-discretization in space of a first order scalar transport equation. For the space discretization we use standard...
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Functional a posteriori error estimates for boundary element methods
Functional error estimates are well-established tools for a posteriori error estimation and related adaptive mesh-refinement for the finite element...
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Error estimates of the backward Euler–Maruyama method for multi-valued stochastic differential equations
In this paper we derive error estimates of the backward Euler–Maruyama method applied to multi-valued stochastic differential equations. An important...
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A Priori Error Estimates and Superconvergence of Splitting Positive Definite Mixed Finite Element Methods for Pseudo-Hyperbolic Integro-Differential Optimal Control Problems
ABSTRACTIn this paper we discuss a priori error estimates and superconvergence of splitting positive definite mixed finite element methods for...
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Residual a Posteriori Error Estimation for Frictional Contact with Nitsche Method
We consider frictional contact problems in small strain elasticity discretized with finite elements and Nitsche method. Both bilateral and unilateral...
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A Posteriori Error Analysis for Pressure-Robust HDG Methods for the Stationary Incompressible Navier–Stokes Equations
A hybridizable discontinuous Galerkin method with divergence-free and H (div)-conforming velocity field is considered in this paper for the stationary...
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A Posteriori Error Control of Approximate Solutions to Boundary Value Problems Found by Neural Networks
The paper discusses how to verify the quality of approximate solutions to partial differential equations constructed by deep neural networks. A...
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A Lagrangian–Eulerian Method on Regular Triangular Grids for Hyperbolic Problems: Error Estimates for the Scalar Case and a Positive Principle for Multidimensional Systems
In this work, we design a new class of fully discrete Lagrangian–Eulerian schemes on triangular grids to approximate nonlinear multidimensional...
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Test Signal Planning for Identifying the Aerodynamic Characteristics of Automatically Controlled Aircraft Taking into Account the Uncertainty of A Priori Data
AbstractWe propose a method for test signal planning for identifying the aerodynamic characteristics of automatically controlled aircraft taking...
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A priori bounds for GIETs, affine shadows and rigidity of foliations in genus two
We prove a rigidity result for foliations on surfaces of genus two, which can be seen as a generalization to higher genus of Herman’s theorem on...
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A-posteriori reduced basis error-estimates for a semi-discrete in space quasilinear parabolic PDE
We prove a-posteriori error-estimates for reduced-order modeling of quasilinear parabolic PDEs with non-monotone nonlinearity. We consider the...
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A posteriori error estimates for the Brinkman–Darcy–Forchheimer problem
In this paper, we study the a posteriori error estimate corresponding to the Brinkman–Darcy–Forchheimer problem. We introduce the variational...
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Optimization of the Cluster-Variant Method of Constructing a Multi-Position Direction Finding System for Conditions of a Priori Uncertainty
AbstractThe possibility of constructing a multi-position direction finding system for the case of a priori uncertainty, based on the application of...
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Optimal Error Estimates of Coupled and Divergence-Free Virtual Element Methods for the Poisson–Nernst–Planck/Navier–Stokes Equations and Applications in Electrochemical Systems
In this article, we propose and analyze a fully coupled, nonlinear, and energy-stable virtual element method (VEM) for solving the coupled...
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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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A priori and a posteriori error analysis of an unfitted HDG method for semi-linear elliptic problems
We present a priori and a posteriori error analysis of a high order hybridizable discontinuous Galerkin (HDG) method applied to a semi-linear...