Publication

Stabilization strategies for high order methods for transport dominated problems

Alfio Quarteroni, Erik Burman, Benjamin Stamm
2008
Journal Articles

Abstract

Standard high order Galerkin methods, such as pure spectral or high order finite element methods, have insufficient stability properties when applied to transport dominated problems. In this paper we review some stabilization strategies for pure spectral methods and spectral multidomain approaches.

Official source

https://infoscience.epfl.ch/entities/publication/d21aa089-0e2a-4f1a-a6bc-dcd6572d6629

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Alfio Quarteroni, Erik Burman, Benjamin Stamm
2008
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/d21aa089-0e2a-4f1a-a6bc-dcd6572d6629

About this result

Related concepts (9)

Finite difference method

In numerical analysis, finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences. Both the spatial domain and time interval (if applicable) are discretized, or broken into a finite number of steps, and the value of the solution at these discrete points is approximated by solving algebraic equations containing finite differences and values from nearby points.

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.

Runge–Kutta methods

In numerical analysis, the Runge–Kutta methods (ˈrʊŋəˈkʊtɑː ) are a family of implicit and explicit iterative methods, which include the Euler method, used in temporal discretization for the approximate solutions of simultaneous nonlinear equations. These methods were developed around 1900 by the German mathematicians Carl Runge and Wilhelm Kutta. The most widely known member of the Runge–Kutta family is generally referred to as "RK4", the "classic Runge–Kutta method" or simply as "the Runge–Kutta method".

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