Choi, Hee Jun

English

This thesis focuses on the development and the analysis of high-order method for Partial Differential Equations (PDEs), the Magneto-HydroDynamics (MHD) equation, the Cahn-Hilliard phase-field equation and the Allen-Cahn phase-field equation and Ordinary Differential Equations (ODEs).  For the fluid related equations, we focus on the stability and the error estimates. We suggest four unconditionally stable discretizations of the MHD equation and perform the error analysis. As an application, we develop an adaptive scheme and carry out numerical experiments to see the effectiveness. We carry out the error analysis of the convex-splitting scheme and the stabilized scheme of the Cahn-Hilliard equation. We develop the spectral method for complex geometries which is based on the fictitious domain method. For the ODEs, we develop a second-order defect correction method. The main tool for the defect correction is the Schur decomposition and the scheme is A-stable

Choi, Heejun

Purdue E-Pubs

On several efficient algorithms for some partial differential equations

ON SEVERAL EFFICIENT ALGORITHMS FOR SOME PARTIAL DIFFERENTIAL EQUATIONS

https://docs.lib.purdue.edu/cgi/viewcontent.cgi?article=2559&amp;context=open_access_dissertations

ON SEVERAL EFFICIENT ALGORITHMS FOR SOME PARTIAL DIFFERENTIAL EQUATIONS

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