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Superconvergence of UWLDG Method for One-Dimensional Linear Sixth-Order Equations
This paper concerns the superconvergence property of the ultraweak-local discontinuous Galerkin (UWLDG) method for one-dimensional linear sixth-order...
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On the superconvergence of a WG method for the elliptic problem with variable coefficients
This article extends a recently developed superconvergence result for weak Galerkin (WG) approximations for modeling partial differential equations...
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Superconvergence and Postprocessing of Collocation Methods for Fractional Differential Equations
This paper aims to propose a complete superconvergence analysis for a postprocessing technique based on collocation methods for fractional...
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Asymptotic Errors in the Superconvergence of Discontinuous Galerkin Methods Based on Upwind-Biased Fluxes for 1D Linear Hyperbolic Equations
In this paper, we study the superconvergence of the semi-discrete discontinuous Galerkin (DG) method for linear hyperbolic equations in one spatial...
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Order two superconvergence of the CDG finite elements for non-self adjoint and indefinite elliptic equations
A conforming discontinuous Galerkin (CDG) finite element method is designed for solving second order non-self adjoint and indefinite elliptic...
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Superconvergence and accuracy enhancement of discontinuous Galerkin solutions for Vlasov–Maxwell equations
This paper explores the discontinuous Galerkin (DG) methods for solving the Vlasov–Maxwell (VM) system, a fundamental model for collisionless...
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Superconvergence analysis of interior penalty discontinuous Galerkin method for a class of time-fractional diffusion problems
In this study, we consider a class of non-autonomous time-fractional partial advection–diffusion-reaction equations with Caputo-type fractional...
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Constructing a CDG Finite Element with Order Two Superconvergence on Rectangular Meshes
A novel conforming discontinuous Galerkin (CDG) finite element method is introduced for Poisson equation on rectangular meshes. This CDG method with...
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Superconvergence Analysis of Curlcurl-Conforming Elements on Rectangular Meshes
In our recent work (Hu et al. in SIAM J Sci Comput 42(6):A3859–A3877, 2020), we observed numerically some superconvergence phenomena of the...
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Unconditional superconvergence analysis of a structure-preserving finite element method for the Poisson-Nernst-Planck equations
In this paper, a linearized structure-preserving Galerkin finite element method is investigated for Poisson-Nernst-Planck (PNP) equations. By making...
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Superconvergence of Newton–Cotes rule for computing hypersingular integral on a circle
In this paper, the composite Newton–Cotes rule for evaluating hypersingular integral on a circle is investigated, we focus on the emphasis of the...
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Unconditional superconvergence analysis of an energy dissipation property preserving nonconforming FEM for nonlinear BBMB equation
In this article, an energy dissipation property preserving modified Crank–Nicolson (CN) fully-discrete scheme is developed and investigated with the...
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Convergence and superconvergence of a fractional collocation method for weakly singular Volterra integro-differential equations
A collocation method for the numerical solution of Volterra integro-differential equations with weakly singular kernels, based on piecewise...
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Unconditionally Superconvergence Error Analysis of an Energy-Stable and Linearized Galerkin Finite Element Method for Nonlinear Wave Equations
In this paper, a linearized energy-stable scalar auxiliary variable (SAV) Galerkin scheme is investigated for a two-dimensional nonlinear wave...
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Unconditional superconvergence analysis of an energy-stable finite element scheme for nonlinear Benjamin–Bona–Mahony–Burgers equation
In this paper, an energy-stable Crank–Nicolson fully discrete finite element scheme is proposed for the Benjamin–Bona–Mahony–Burgers equation....
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Superconvergence of Direct Discontinuous Galerkin Methods: Eigen-structure Analysis Based on Fourier Approach
This paper investigates superconvergence properties of the direct discontinuous Galerkin (DDG) method with interface corrections and the symmetric...
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Convergence and superconvergence analysis of finite element methods for nonlinear Ginzburg–Landau equation with Caputo derivative
In this paper, we study and analyze the time fractional Ginzburg–Landau equation (FGLE) using finite element methods (FEMs) in space and L 1 scheme in...
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Superconvergence analysis of a two-grid finite element method for nonlinear time-fractional diffusion equations
Based on spatial finite-element methods combined with classical L1 time step** method, the superconvergence analysis of the two-grid approximate...
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Superconvergence Analysis of a Robust Orthogonal Gauss Collocation Method for 2D Fourth-Order Subdiffusion Equations
In this paper, we study the orthogonal Gauss collocation method (OGCM) with an arbitrary polynomial degree for the numerical solution of a...
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Optimal superconvergence analysis for the Crouzeix-Raviart and the Morley elements
In this paper, an improved superconvergence analysis is presented for both the Crouzeix-Raviart element and the Morley element. The main idea of the...