In this thesis the connections between the boundary conditions and the vari- ance of the solution to a stochastic partial differential equation (PDE) are investigated. In particular a hyperbolical system of PDE’s with stochastic initial and boundary data are considered. The problem is shown to be well- posed on a class of boundary conditions through the energy method. Stability is shown by using summation-by-part operators coupled with simultaneous- approximation-terms. By using the energy estimates, the relative variance of the solutions for different boundary conditions are analyzed. It is concluded that some types of boundary conditions yields a lower variance than others. This is verified by numerical computations.
Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:liu-70355 |
Date | January 2011 |
Creators | Arndt, Carl-Fredrik |
Publisher | Linköpings universitet, Beräkningsvetenskap |
Source Sets | DiVA Archive at Upsalla University |
Language | English |
Detected Language | English |
Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
Format | application/pdf |
Rights | info:eu-repo/semantics/openAccess |
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