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Optimal error estimates of the semidiscrete discontinuous Galerkin methods for two dimensional hyperbolic equations on Cartesian meshes using Pk elements
- Source :
- ESAIM: Mathematical Modelling and Numerical Analysis. 54:705-726
- Publication Year :
- 2020
- Publisher :
- EDP Sciences, 2020.
-
Abstract
- In this paper, we study the optimal error estimates of the classical discontinuous Galerkin method for time-dependent 2-D hyperbolic equations using Pk elements on uniform Cartesian meshes, and prove that the error in the L2 norm achieves optimal (k + 1)th order convergence when upwind fluxes are used. For the linear constant coefficient case, the results hold true for arbitrary piecewise polynomials of degree k ≥ 0. For variable coefficient and nonlinear cases, we give the proof for piecewise polynomials of degree k = 0, 1, 2, 3 and k = 2, 3, respectively, under the condition that the wind direction does not change. The theoretical results are verified by numerical examples.
- Subjects :
- Numerical Analysis
Constant coefficients
Degree (graph theory)
Applied Mathematics
010103 numerical & computational mathematics
01 natural sciences
law.invention
010101 applied mathematics
Computational Mathematics
Nonlinear system
Discontinuous Galerkin method
law
Modeling and Simulation
Convergence (routing)
Piecewise
Applied mathematics
Cartesian coordinate system
0101 mathematics
Hyperbolic partial differential equation
Analysis
Mathematics
Subjects
Details
- ISSN :
- 12903841 and 0764583X
- Volume :
- 54
- Database :
- OpenAIRE
- Journal :
- ESAIM: Mathematical Modelling and Numerical Analysis
- Accession number :
- edsair.doi...........68b16076f34970d30b00ab5415855731