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Discontinuous Galerkin methods for Stokes equations under power law slip boundary condition: a priori analysis
In this work, three discontinuous Galerkin (DG) methods are formulated and analysed to solve Stokes equations with power law slip boundary condition....
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On a discontinuous nonlinear elliptic problem of nonlocal-type with Neumann boundary condition
The objective of this article is to investigate the existence of a weak solution to a class of nonlocal-type problem with Neumann boundary condition,...
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A Quadratic Discontinuous Finite Volume Element Scheme for Stokes Problems
In this paper, we construct a quadratic discontinuous finite volume scheme for Stokes equations. Specifically, the quadratic discontinuous finite...
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The Riemann problem for isentropic compressible Euler equations with discontinuous flux
We consider the singular Riemann problem for the rectilinear isentropic compressible Euler equations with discontinuous flux, more specifically, for...
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A Birkhoff–Kellogg Type Theorem for Discontinuous Operators with Applications
By means of fixed point index theory for multivalued maps, we provide an analogue of the classical Birkhoff–Kellogg Theorem in the context of...
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Hybridizable Discontinuous Galerkin Methods for the Two-Dimensional Monge–Ampère Equation
We introduce two hybridizable discontinuous Galerkin (HDG) methods for numerically solving the two-dimensional Monge–Ampère equation. The first HDG...
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Application of the Hausdorff Metric in Model Problems with Discontinuous Functions in Boundary Conditions
Using an example of the Cauchy problem for the one-dimensional heat equation, we study the approximation of the solution to the initial condition in...
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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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A Note on Gradient Estimates for Elliptic Equations with Discontinuous Coefficients
The authors will use a method in metric geometry to show an L p -estimate for gradient of the weak solutions to elliptic equations with discontinuous...
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Coupling of direct discontinuous Galerkin method and natural boundary element method for exterior interface problems with curved elements
This paper presents the coupling method of direct discontinuous Garlekin (DDG) and natural boundary element (NBE) for exterior interface problem. The...
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Inverse resonance problems with the discontinuous conditions
In this paper, we consider the inverse resonance problems for the discontinuous and non-selfadjoint Sturm-Liouville problem. We prove the uniqueness...
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Discontinuous Galerkin Methods for Hemivariational Inequalities in Contact Mechanics
In this paper, we study discontinuous Galerkin (DG) methods for solving two contact problems. The first problem involves a frictionless normal...
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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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Limit Cycle Bifurcations Near Nonsmooth Homoclinic Cycle in Discontinuous Systems
The main aim of this paper is to study the limit cycle bifurcations near the homoclinic cycle in the discontinuous systems. Based on the impoved...
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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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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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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 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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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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On the Accuracy of Discontinuous Galerkin Method Calculating Gas-Dynamic Shock Waves
AbstractThe results of a numerical calculation of gas-dynamic shock waves that arise in solving the Cauchy problem with smooth periodic initial data...
