Add to ORKGThe new concept of numerical smoothness is applied to the RKDG (Runge-Kutta/Discontinuous Galerkin) methods for scalar nonlinear conservations laws. The main result is an a posteriori error estimate for the RKDG methods of arbitrary order in space and time, with optimal convergence rate. In this paper, the case of smooth solutions is the focus point. However, the error analysis framework is prepared to deal with discontinuous solutions in the future.
In this paper, we analyze the Lax–Wendroff discontinuous Galerkin (LWDG) method for solving linear c...
This is the fifth paper in a series in which we construct and study the so-called Runge–Kutta discon...
AbstractA posteriori error estimates are derived for a stabilized discontinuous Galerkin method (DGM...
In [28] and [13], an error estimate of optimal convergence rates and optimal error propagation (opti...
The error analysis for the Runge-Kutta discontinuous Galerkin (RKDG) method for solving the scalar n...
Abstract. Discontinuities usually appear in solutions of nonlinear conservation laws even though the...
In this paper, we discuss the stability and error estimates of the fully discrete schemes for linear...
In this paper, we discuss the stability and error estimates of the fully discrete schemes for linear...
In this paper, we review the development of the Runge-Kutta discontinuous Galerkin (RKDG) methods fo...
This is the fifth paper in a series in which we construct and study the so-called Runge-Kutta Discon...
AbstractA smoothness/shock indicator is proposed for the RKDG methods solving nonlinear conservation...
In this paper, we review the development of the Runge–Kutta discontinuous Galerkin (RKDG) methods fo...
In this paper we present an a priori error estimate of the Runge–Kutta discontinuous Galerkin method...
In this paper we present an a priori error estimate of the Runge–Kutta discontinuous Galerkin method...
In an effort to improve the error analysis of numerical methods for time-dependent PDEs and obtain r...
In this paper, we analyze the Lax–Wendroff discontinuous Galerkin (LWDG) method for solving linear c...
This is the fifth paper in a series in which we construct and study the so-called Runge–Kutta discon...
AbstractA posteriori error estimates are derived for a stabilized discontinuous Galerkin method (DGM...
In [28] and [13], an error estimate of optimal convergence rates and optimal error propagation (opti...
The error analysis for the Runge-Kutta discontinuous Galerkin (RKDG) method for solving the scalar n...
Abstract. Discontinuities usually appear in solutions of nonlinear conservation laws even though the...
In this paper, we discuss the stability and error estimates of the fully discrete schemes for linear...
In this paper, we discuss the stability and error estimates of the fully discrete schemes for linear...
In this paper, we review the development of the Runge-Kutta discontinuous Galerkin (RKDG) methods fo...
This is the fifth paper in a series in which we construct and study the so-called Runge-Kutta Discon...
AbstractA smoothness/shock indicator is proposed for the RKDG methods solving nonlinear conservation...
In this paper, we review the development of the Runge–Kutta discontinuous Galerkin (RKDG) methods fo...
In this paper we present an a priori error estimate of the Runge–Kutta discontinuous Galerkin method...
In this paper we present an a priori error estimate of the Runge–Kutta discontinuous Galerkin method...
In an effort to improve the error analysis of numerical methods for time-dependent PDEs and obtain r...
In this paper, we analyze the Lax–Wendroff discontinuous Galerkin (LWDG) method for solving linear c...
This is the fifth paper in a series in which we construct and study the so-called Runge–Kutta discon...
AbstractA posteriori error estimates are derived for a stabilized discontinuous Galerkin method (DGM...