Publication

A Local Discontinuous Galerkin Method for Two-Dimensional Time Fractional Diffusion Equations

Jan Sickmann Hesthaven, Reza Mokhtari
2020
Journal Articles

Abstract

For two-dimensional (2D) time fractional diffusion equations, we construct a numerical method based on a local discontinuous Galerkin (LDG) method in space and a finite difference scheme in time. We investigate the numerical stability and convergence of the method for both rectangular and triangular meshes and show that the method is unconditionally stable. Numerical results indicate the effectiveness and accuracy of the method and confirm the analysis.

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https://infoscience.epfl.ch/entities/publication/e5dd2d3c-1348-47da-a3ec-6d422f49677a

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Jan Sickmann Hesthaven, Reza Mokhtari
2020
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/e5dd2d3c-1348-47da-a3ec-6d422f49677a

About this result

Related concepts (13)

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.

Numerical stability

In the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues.

Numerical methods for ordinary differential equations

Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.

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