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Numerical Reconstruction of a Discontinuous Diffusive Coefficient in Variable-Order Time-Fractional Subdiffusion
We consider a discontinuous coefficient reconstruction problem associated with a variable-order time-fractional subdiffusion equation. Both interface...
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Hybridizable discontinuous Galerkin reduced order model for the variable coefficient advection equation
In this paper, a hybridizable discontinuous Galerkin (HDG) model order reduction technique is proposed to solve the variable coefficient advection...
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Compact Approximation of a Two-Dimensional Boundary Value Problem for Elliptic Equations of the Second Order with a Discontinuous Coefficient
AbstractFor an elliptic equation of the second order with variable discontinuous coefficients and the right side, a scheme of the fourth order of...
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Distributions of Functionals of the Local Time of Brownian Motion with Discontinuous Drift
Diffusion with piecewise constant drift and diffusion coefficient 1 is considered. Such a process is called the Brownian motion with discontinuous...
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Approximation to the Sturm–Liouville Problem with a Discontinuous Nonlinearity
AbstractWe consider a continuous approximation to the Sturm–Liouville problem with a nonlinearity discontinuous in the phase variable. The...
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Distributions of Functionals of a Skew Brownian motion with Discontinuous Drift
A skew Brownian motion with piecewise constant drift is considered. This diffusion includes a skew Brownian motion with linear drift with equal...
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Robust Flux Reconstruction and a Posteriori Error Analysis for an Elliptic Problem with Discontinuous Coefficients
In this paper, we locally construct a conservative flux for finite element solutions of elliptic interface problems with discontinuous coefficients....
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Discontinuous Galerkin Methods for Network Patterning Phase-Field Models
In this paper, we propose a class of discontinuous Galerkin methods under the scalar auxiliary variable framework (SAV-DG) to solve a biological...
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A Generalized Framework for Direct Discontinuous Galerkin Methods for Nonlinear Diffusion Equations
In this study, we propose a unified, general framework for the direct discontinuous Galerkin methods. In the new framework, the antiderivative of the...
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A Local Discontinuous Galerkin Method for Time-Fractional Diffusion Equations
In this paper, a local discontinuous Galerkin (LDG) scheme for the time-fractional diffusion equation is proposed and analyzed. The Caputo...
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Solving Nonlinear Volterra Integral Equations of the First Kind with Discontinuous Kernels by Using the Operational Matrix Method
AbstractA numerical method to solve the nonlinear Volterra integral equations of the first kind with discontinuous kernels is proposed. Usage of...
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A radial integration displacement discontinuity method with discontinuous isoparametric elements for 3D fracture simulations
To improve the accuracy of displacement discontinuity method and enhance its adaptivity, a general-purpose 3D displacement discontinuity method with...
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Discontinuous Galerkin Method Based on the Reduced Space for the Nonlinear Convection–Diffusion–Reaction Equation
In this paper, by introducing a reconstruction operator based on the Legendre moments, we construct a reduced discontinuous Galerkin (RDG) space that...
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A Quadratic B-Spline Collocation Method for a Singularly Perturbed Semilinear Reaction–Diffusion Problem with Discontinuous Source Term
In this paper, a quadratic B-spline collocation method is developed to solve a singularly perturbed semilinear reaction–diffusion problem with a...
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Two-level Schwarz Methods for Hybridizable Discontinuous Galerkin Methods
In this paper, we propose two-level domain decomposition methods for hybridizable discontinuous Galerkin discretizations including hybridized local...
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The High-Order Variable-Coefficient Explicit-Implicit-Null Method for Diffusion and Dispersion Equations
For the high-order diffusion and dispersion equations, the general practice of the explicit-implicit-null (EIN) method is to add and subtract an...
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Discontinuous stationary solutions to certain reaction-diffusion systems
Systems consisting of a single ordinary differential equation coupled with one reaction-diffusion equation in a bounded domain and with the Neumann...
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Discontinuous Galerkin Methods for Linear Hyperbolic Systems
We develop a space-time method with a discontinuous Galerkin discretization in space for linear wave problems. For the ansatz space we use piecewise...
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A discontinuous Galerkin method for Maxwell’s transmission eigenvalue problem
We propose an interior penalty discontinuous Galerkin (IPDG) method for the Maxwell’s transmission eigenvalue problem. First we reformulate the...
