Mixed finite-element method for strongly nonlinear elliptic problems: The h-p - version
Abstract
Mixed finite element methods for strongly nonlinear second order elliptic problems are proposed and analyzed. Existence and uniqueness of the approximate solution are demonstrated using a fixed point argument. Convergence and stability of the method are proved both with respect to mesh refinement and increase of the degree of the approximating polynomials. The analysis is carried out in detail using Raviart-Thomas-Nedelec spaces as an example. Numerical results for minimal surface problems are obtained using Brezzi-Douglas-Marini spaces. Graphs of the approximate solutions are presented for various problems.
Degree
Ph.D.
Advisors
Milner, Purdue University.
Subject Area
Mathematics
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