Hp- FEM: Finite Element Method, Numerical Analysis, Partial Differential Equation, Approximation - Softcover

 
9786131334405: Hp- FEM: Finite Element Method, Numerical Analysis, Partial Differential Equation, Approximation

Synopsis

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The hp-FEM is a general version of the finite element method (FEM), a numerical method for solving partial differential equations based on piecewise-polynomial approximations that employs elements of variable size (h) and polynomial degree (p). The origins of hp-FEM date back to the pioneering work of Ivo Babuska et al. Who discovered that the finite element method converges exponentially fast when the mesh is refined using a suitable combination of h-refinements (dividing elements into smaller ones) and p-refinements (increasing their polynomial degree). The exponential convergence makes the method a very attractive choice compared to most other finite element methods which only converge with an algebraic rate. The exponential convergence of the hp-FEM was not only predicted theoretically but also observed by numerous independent researchers.

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