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    Galerkin Projections Between Finite Element Spaces

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    Thompson_RA_T_2015.pdf (676.5Kb)
    Downloads: 7181
    Date
    2015-06-17
    Author
    Thompson, Ross Anthony
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    Abstract
    Adaptive mesh refinement schemes are used to find accurate low-dimensional approximating spaces when solving elliptic PDEs with Galerkin finite element methods. For nonlinear PDEs, solving the nonlinear problem with Newton's method requires an initial guess of the solution on a refined space, which can be found by interpolating the solution from a previous refinement. Improving the accuracy of the representation of the converged solution computed on a coarse mesh for use as an initial guess on the refined mesh may reduce the number of Newton iterations required for convergence. In this thesis, we present an algorithm to compute an orthogonal L^2 projection between two dimensional finite element spaces constructed from a triangulation of the domain. Furthermore, we present numerical studies that investigate the efficiency of using this algorithm to solve various nonlinear elliptic boundary value problems.
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    http://hdl.handle.net/10919/52968
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    • Masters Theses [21552]

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