This is an extended version of my PhD thesis which extends the theory of finite element exterior calculus (FEEC) to parabolic evolution equations. In the extended version, I explore some more precise visualizations of the defined quantities, as well as explain how the modern theory of functional analysis applies. In the main part, I extend the theory of approximating evolution equations in Euclidean space (using FEEC) to hypersurfaces. After these main results, I describe some possible extensions to nonlinear equations. A few appendices detail one of the original motivations for getting into this theory in the first place: canonical geometries given as steady state solutions and extremals of certain functionals.
Computation and Visualization of Geometric Partial Differential Equations
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This is an extended version of my PhD thesis which extends the theory of finite element exterior calculus (FEEC) to parabolic evolution equations. In the extended version, I explore some more precise visualizations of the defined quantities, as well as explain how the modern theory of functional analysis applies. In the main part, I extend the theory of approximating evolution equations in Euclidean space (using FEEC) to hypersurfaces. After these main results, I describe some possible extensions to nonlinear equations. A few appendices detail one of the original motivations for getting into this theory in the first place: canonical geometries given as steady state solutions and extremals of certain functionals.
Elementary Mathematics for Geometric Design.-Introduction to Geometric Design.-Introduction to Partial Differential Equations.-Elliptic PDEs for Geometric Design.-Interactive Design.-Parametric...
This text teaches finite element methods and basic finite difference methods from a computational point of view. It emphasizes developing flexible computer programs using the numerical library...
This book is not a textbook, but rather a coherent collection of papers from the field of partial differential equations. Nevertheless we believe that it may very well serve as a good introduction...
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