A priori and a posteriori error analysis of the first order hyperbolic equation by using DG method
Muhammad Shakhawat Hossain1, Chunguang Xiong1, Huafei Sun1
1Department of Mathematics, Beijing Institute of Technology, Beijing, China.
Abstract:
In this research article, a discontinuous Galerkin method with a weighted parameter θ and a penalty parameter γ is proposed for solving the first order hyperbolic equation. The key aim of this method is to design an error estimation for both a priori and a posteriori error analysis on general finite element meshes. It is also exposed to the reliability and effectiveness of both parameters in the order of convergence of the solutions. For a posteriori error estimation, residual adaptive mesh- refining algorithm is employed. A series of numerical experiments are illustrated that demonstrate the efficiency of the method.
More Related Videos
13:44Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
Published on: August 30, 2013
09:01Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
Published on: April 4, 2017
Related Concept Videos
Second Order systems II
Bernoulli's Equation: Problem Solving
The first step is to compute the cross-sectional areas of the pipe and the Venturi throat to analyze the pressure difference indicated by the pressure gauge. Next, the continuity...
Second Derivatives and Laplace Operator
Consider a scalar function. The curl of its...
Bernoulli's Equation
Routh-Hurwitz Criterion II
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
Accuracy, limits, and approximation
Accuracy is defined as the closeness of the measured value to the true or actual value. In engineering mechanics, repeated measurements are taken during theoretical or experimental analyses to ensure that the result is precise and accurate.
The accuracy of any solution is based on the...
