Semi-discrete and fully discrete HDG methods for Burgers' equation

Semi-Discrete Formulations for 1D Burgers Equation

In this work we compare semi-discrete formulations to obtain numerical solutions for the 1D Burgers equation. The formulations consist in the discretization of the time-domain via multi-stage methods of second and fourth order: R11 and R22 Padé approximants, and of the spatial-domain via finite element methods: least-squares (MEFMQ), Galerkin (MEFG) and Streamline-Upwind Petrov-Galerkin (SUPG)....

Discrete Burgers' Equation, Binomial Coefficients and Mandala

Discrete analogue of the Burgers equation

We propose the set of coupled ordinary differential equations dnj/dt = nj−1 − nj as a discrete analogue of the classic Burgers equation. We focus on traveling waves and triangular waves, and find that these special solutions of the discrete system capture major features of their continuous counterpart. In particular, the propagation velocity of a traveling wave and the shape of a triangular wav...

Discrete Analog of the Burgers Equation

We propose the set of coupled ordinary differential equations dnj/dt = n 2 j−1 − n 2 j as a discrete analog of the classic Burgers equation. We focus on traveling waves and triangular waves, and find that these special solutions of the discrete system capture major features of their continuous counterpart. In particular, the propagation velocity of a traveling wave and the shape of a triangular...

DISCRETE SIZE AND DISCRETE-CONTINUOUS CONFIGURATION OPTIMIZATION METHODS FOR TRUSS STRUCTURES USING THE HARMONY SEARCH ALGORITHM

Many methods have been developed for structural size and configuration optimization in which cross-sectional areas are usually assumed to be continuous. In most practical structural engineering design problems, however, the design variables are discrete. This paper proposes two efficient structural optimization methods based on the harmony search (HS) heuristic algorithm that treat both discret...