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dc.contributor.authorOlderkjær, Daniel Stensrudeng
dc.date.accessioned2014-08-27T09:16:06Z
dc.date.available2014-08-27T09:16:06Z
dc.date.issued2014-06-02eng
dc.date.submitted2014-06-02eng
dc.identifier.urihttps://hdl.handle.net/1956/8353
dc.description.abstractIn this thesis we prove the multi-point flux approximation O-method (MPFA) to yield exact potential and flux for the trigonometric potential functions u(x,y)=sin(x)sin(y) and u(x,y)=cos(x)cos(y). This is done on uniform square grids in a homogeneous medium with principal directions of the permeability aligned with the grid directions when having periodic boundary conditions. Earlier theoretical and numerical convergence articles suggests that these potential functions should only yield second order convergence. Hence, our motivation for the analysis was to gain new insight into the convergence of the method, as well as to develop theoretical proofs for what seems as decent examples for testing implementation. An extension of the result to uniform rectangular grids in an isotropic medium is also briefly discussed, before we develop a numerical overview of the exactness phenomenon for different types of boundary conditions. Lastly, an investigation of application of these results to obtain exact potential and flux using the MPFA method for general potential functions approximated by Fourier series was conducted.en_US
dc.format.extent726332 byteseng
dc.format.mimetypeapplication/pdfeng
dc.language.isoengeng
dc.publisherThe University of Bergenen_US
dc.subjectMPFAeng
dc.subjectFluxeng
dc.subjectMulti-pointeng
dc.subjectApproximationeng
dc.subjectO-methodeng
dc.subjectSuperconvergenteng
dc.subjectExacteng
dc.titleExact and Superconvergent Solutions of the Multi-Point Flux Approximation O-method: Analysis and Numerical Testsen_US
dc.typeMaster thesis
dc.rights.holderCopyright the author. All rights reserveden_US
dc.description.degreeMaster i Anvendt og beregningsorientert matematikken_US
dc.description.localcodeMAMN-MAB
dc.description.localcodeMAB399
dc.subject.nus753109eng
fs.subjectcodeMAB399


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