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The Finite Difference Methods for Multi-phase Free Boundary ProblemsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2011 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Stockholm: KTH Royal Institute of Technology , 2011. , vii, 23 p.
##### Series

Trita-MAT. MA, ISSN 1401-2278 ; 11:02
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-33543OAI: oai:DiVA.org:kth-33543DiVA: diva2:415959
##### Public defence

2011-05-12, Sal F3., Lindstedtsvägen 26. KTH, Stocokholm, 13:00 (English)
##### Opponent

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##### Supervisors

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#####

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##### Note

QC 20110510Available from: 2011-05-10 Created: 2011-05-10 Last updated: 2011-08-11Bibliographically approved
##### List of papers

This thesis consist of an introduction and four research papers concerning numerical analysis for a certain class of free boundary problems.

Paper I is devoted to the numerical analysis of the so-called two-phase membrane problem. Projected Gauss-Seidel method is constructed. We prove general convergence of the algorithm as well as obtain the error estimate for the finite difference scheme.

In Paper II we have improved known results on the error estimates for a Classical Obstacle (One-Phase) Problem with a finite difference scheme.

Paper III deals with the parabolic version of the two-phase obstacle-like problem. We introduce a certain variational form, which allows us to definea notion of viscosity solution. The uniqueness of viscosity solution is proved, and numerical nonlinear Gauss-Seidel method is constructed.

In the last paper, we study a numerical approximation for a class of stationary states for reaction-diffusion system with m densities having disjoint support. The proof of convergence of the numerical method is given in some particular cases. We also apply our numerical simulations for the spatial segregation limit of diffusive Lotka-Volterra models in presence of high competition and inhomogeneous Dirichlet boundary conditions.

1. Numerical Solution of the Two-Phase Obstacle Problem by Finite Difference Method$(function(){PrimeFaces.cw("OverlayPanel","overlay416068",{id:"formSmash:j_idt1143:0:j_idt1147",widgetVar:"overlay416068",target:"formSmash:j_idt1143:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. An Error Estimate for the Finite Difference Scheme for One-Phase Obstacle Problem$(function(){PrimeFaces.cw("OverlayPanel","overlay416150",{id:"formSmash:j_idt1143:1:j_idt1147",widgetVar:"overlay416150",target:"formSmash:j_idt1143:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. The Finite Difference Method for Two-Phase Parabolic Obstacle-Like Problem: Like Problem$(function(){PrimeFaces.cw("OverlayPanel","overlay416154",{id:"formSmash:j_idt1143:2:j_idt1147",widgetVar:"overlay416154",target:"formSmash:j_idt1143:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. Numerical Algorithms for a Variational problem of the Spatial Segregation of Reaction-diffusion Systems$(function(){PrimeFaces.cw("OverlayPanel","overlay416157",{id:"formSmash:j_idt1143:3:j_idt1147",widgetVar:"overlay416157",target:"formSmash:j_idt1143:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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