Abstract
In this paper, we introduce and investigate the performance of a hybridizable discontinuous Galerkin (HDG) method for approximating the solution of conservative fractional diffusion equations (CFDE). The main attractive feature of these methods is the fact that the only globally coupled unknowns are those at the element boundaries. We first introduce the HDG method for the CFDE and prove the existence and uniqueness of the numerical solution provided that the stabilization parameter is strictly positive. We provide extensive numerical results to test the convergence behavior of the HDG approximation.
Keywords
Mathematics
Discontinuous Galerkin method
Uniqueness
Convergence (economics)
Applied mathematics
Diffusion
Weak formulation
Mathematical analysis
Finite element method
Boundary value problem
Subject Areas
Fractional Differential Equations Solutions
·Modeling and Simulation ·Physical Sciences
Advanced Numerical Methods in Computational Mathematics
·Computational Mechanics ·Physical Sciences
Differential Equations and Numerical Methods
·Numerical Analysis ·Physical Sciences
Citations by Year
2019: 2
2022: 1
2025: 1
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