Finite Element Solutions to Nonlinear Partial Differential Equations

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This paper develops a numerical algorithm that produces finite element solutions for a broad class of partial differential equations. The method is based on steepest descent methods in the Sobolev space H¹(Ω). Although the method may be applied in more general settings, we consider only differential equations that may be written as a first order quasi-linear system. The method is developed in a Hilbert space setting where strong convergence is established for part of the iteration. We also prove convergence for an inner iteration in the finite element setting. The method is demonstrated on Burger's equation and the Navier-Stokes equations ... continued below

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vi, 52 leaves : ill.

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Beasley, Craig J. (Craig Jackson) August 1981.

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  • Beasley, Craig J. (Craig Jackson)

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This paper develops a numerical algorithm that produces finite element solutions for a broad class of partial differential equations. The method is based on steepest descent methods in the Sobolev space H¹(Ω). Although the method may be applied in more general settings, we consider only differential equations that may be written as a first order quasi-linear system. The method is developed in a Hilbert space setting where strong convergence is established for part of the iteration. We also prove convergence for an inner iteration in the finite element setting. The method is demonstrated on Burger's equation and the Navier-Stokes equations as applied to the square cavity flow problem. Numerical evidence suggests that the accuracy of the method is second order,. A documented listing of the FORTRAN code for the Navier-Stokes equations is included.

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vi, 52 leaves : ill.

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  • August 1981

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  • Aug. 22, 2014, 6 p.m.

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  • July 2, 2018, 10:38 a.m.

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Beasley, Craig J. (Craig Jackson). Finite Element Solutions to Nonlinear Partial Differential Equations, dissertation, August 1981; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc331330/: accessed July 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .