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A Mass-Conservative Reduced-Order Algorithm in Solving Optimal Control of Convection-Diffusion Equation
This paper introduces a novel approach, the mass-conservative reduced-order characteristic finite element (MCROCFE) method, designed for optimal...
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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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Weakly Compressible Two-Layer Shallow-Water Flows Along Channels
In this paper, we formulate a model for weakly compressible two-layer shallow water flows with friction in general channels. The formulated model is...
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Gradient-Based Monte Carlo Methods for Relaxation Approximations of Hyperbolic Conservation Laws
Particle methods based on evolving the spatial derivatives of the solution were originally introduced to simulate reaction-diffusion processes,...
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A Penalty-Free and Essentially Stabilization-Free DG Method for Convection-Dominated Second-Order Elliptic Problems
A new discontinuous Galerkin (DG) method is proposed and analyzed for general second-order elliptic problems. It features that local
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A Combined Mixed Hybrid and Hybridizable Discontinuous Galerkin Method for Darcy Flow and Transport
A combined hybrid mixed and hybridizable discontinuous Galerkin method is formulated for the flow and transport equations. Convergence of the method...
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Gradient-Robust Hybrid DG Discretizations for the Compressible Stokes Equations
This paper studies two hybrid discontinuous Galerkin (HDG) discretizations for the velocity-density formulation of the compressible Stokes equations...
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Error Analysis of Serendipity Virtual Element Methods for Semilinear Parabolic Integro-Differential Equations
The main objective of this study is to evaluate the performance of serendipity virtual element methods in solving semilinear parabolic...
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A Parallel Finite Element Discretization Scheme for the Natural Convection Equations
This article presents a parallel finite element discretization scheme for solving numerically the steady natural convection equations, where a fully...
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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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Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport
We introduce an hp -version discontinuous Galerkin finite element method (DGFEM) for the linear Boltzmann transport problem. A key feature of this new...
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Anisotropic Weakly Over-Penalised Symmetric Interior Penalty Method for the Stokes Equation
In this study, we investigate an anisotropic weakly over-penalised symmetric interior penalty method for the Stokes equation on convex domains. Our...
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Discretization of Non-uniform Rational B-Spline (NURBS) Models for Meshless Isogeometric Analysis
We present an algorithm for fast generation of quasi-uniform and variable-spacing nodes on domains whose boundaries are represented as computer-aided...
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The Splitting Characteristic Finite Difference Domain Decomposition Scheme for Solving Time-Fractional MIM Nonlinear Advection–Diffusion Equations
In this paper, we develop a new splitting characteristic finite difference scheme for solving the time-fractional mobile-immobile nonlinear...
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A Robust Randomized Indicator Method for Accurate Symmetric Eigenvalue Detection
We propose a robust randomized indicator method for the reliable detection of eigenvalue existence within an interval for symmetric matrices A . An...
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A Multiscale Finite Element Method for an Elliptic Distributed Optimal Control Problem with Rough Coefficients and Control Constraints
We construct and analyze a multiscale finite element method for an elliptic distributed optimal control problem with pointwise control constraints,...
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On the Immersed Boundary Method with Time-Filter-SAV for Solving Fluid–Structure Interaction Problem
In this work, the immersed boundary method with time filter and scalar auxiliary variable techniques is studied to solve the fluid–structure...
