Publication

MATHICSE Technical Report : Nitsche’s method for parabolic Partial Differential Equations with mixed time varying boundary conditions

Alfio Quarteroni
2015
Working Papers

Abstract

We investigate a finite element approximation of an initial boundary value problem associated with parabolic Partial Differential Equations endowed with mixed time varying boundary conditions, switching from essential to natural and viceversa. The switching occurs both in time and in different portions of the boundary. For this problem, we apply and extend the Nitsche’s method presented in [Juntunen and Stenberg, Mathematics of Computation, 2009] to the case of mixed time varying boundary conditions. After proving existence and numerical stability of the full discrete numerical solution obtained by using the θ-method for time discretization, we present and discuss a numerical test that compares our method to a standard approach based on remeshing and projection procedures.

Official source

https://infoscience.epfl.ch/entities/publication/a4748aaf-01c3-4aa0-9a3d-d005521416fb

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Alfio Quarteroni
2015
Working Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/a4748aaf-01c3-4aa0-9a3d-d005521416fb

About this result

Related concepts (32)

Boundary value problem

In the study of differential equations, a boundary-value problem is a differential equation subjected to constraints called boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions. Boundary value problems arise in several branches of physics as any physical differential equation will have them. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems.

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 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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MATHICSE Technical Report : Nitsche’s method for parabolic Partial Differential Equations with mixed time varying boundary conditions

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