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Superconvergence of the local discontinuous Galerkin method for nonlinear convection-diffusion problems [PDF]
Journal of Inequalities and Applications, 2017 In this paper, we discuss the superconvergence of the local discontinuous Galerkin methods for nonlinear convection-diffusion equations. We prove that the numerical solution is ( k + 3 / 2 ) $(k+3/2)$ th-order superconvergent to a particular projection ...
Hui Bi, Chengeng Qian
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Superconvergence of semidiscrete finite element methods for bilinear parabolic optimal control problems [PDF]
Journal of Inequalities and Applications, 2017 In this paper, a semidiscrete finite element method for solving bilinear parabolic optimal control problems is considered. Firstly, we present a finite element approximation of the model problem.
Yuelong Tang, Yuchun Hua
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Time-dependent Hamiltonian Simulation of Highly Oscillatory Dynamics and Superconvergence for Schrödinger Equation [PDF]
Quantum, 2022 We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators.
Dong An, Di Fang, Lin Lin
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Convergence of Collocation Methods for One Class of Impulsive Delay Differential Equations
Axioms, 2023 This paper is concerned with collocation methods for one class of impulsive delay differential equations (IDDEs). Some results for the convergence, global superconvergence and local superconvergence of collocation methods are given.
Zhiwei Wang, Guilai Zhang, Yang Sun
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Spectral approximation methods for Fredholm integral equations with non-smooth kernels
Mathematical Modelling and Analysis, 2022 In this paper, polynomially based projection and modified projection methods for approximating the solution of Fredholm integral equations with a kernel of Green’s function type are studied.
Chafik Allouch +2 more
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Journal of Mathematics, 2021 The classical composite midpoint rectangle rule for computing Cauchy principal value integrals on an interval is studied. By using a piecewise constant interpolant to approximate the density function, an extended error expansion and its corresponding ...
Chunxiao Yu, Lingling Wei
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Superconvergence for Multistep Collocation [PDF]
Mathematics of Computation, 1989 One-step collocation methods are known to be a subclass of implicit Runge-Kutta methods. Further, one-leg methods are special multistep one-point collocation methods. In this paper we extend both of these collocation ideas to multistep collocation methods with k previous meshpoints and m collocation points. By construction, the order is at least
Lie, Ivar, Nørsett, Syvert P.
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AIMS Mathematics, 2023 This study focused on the superconvergence of the finite element method for the five-dimensional Poisson equation in the $ W^{1, \infty} $-seminorm. Specifically, we investigated the block finite element method, which is a tensor-product finite element ...
Jinghong Liu
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AIMS Mathematics, 2022 This paper aims to construct a two-grid mixed finite element scheme for distributed optimal control governed by semilinear elliptic equations. The state and co-state are approximated by the $ P_0^2 $-$ P_1 $ pair and the control variable is approximated ...
Changling Xu, Hongbo Chen
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Electronic Research Archive, 2023 In this paper, we present a two-grid scheme of fully discrete finite element approximation for optimal control problems governed by parabolic integro-differential equations. The state and co-state variables are approximated by a piecewise linear function
Changling Xu , Huilai Li
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