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Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
Services
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I. Basic math.
II. Pricing and Hedging.
III. Explicit techniques.
IV. Data Analysis.
V. Implementation tools.
VI. Basic Math II.
VII. Implementation tools II.
1. Calculational Linear Algebra.
2. Wavelet Analysis.
3. Finite element method.
A. Tutorial introduction into finite element method.
B. Finite elements for Poisson equation with Dirichlet boundary conditions.
C. Finite elements for Heat equation with Dirichlet boundary conditions.
D. Finite elements for Heat equation with Neumann boundary conditions.
a. Weak formulation for Neumann boundary conditions. Natural and essential boundary conditions.
E. Relaxed boundary conditions for approximation spaces.
F. Convergence of finite elements applied to nonsmooth data.
G. Convergence of finite elements for generic parabolic operator.
4. Construction of approximation spaces.
5. Time discretization.
6. Variational inequalities.
VIII. Bibliography
Notation. Index. Contents.

Finite elements for Heat equation with Neumann boundary conditions.


roblem

(Heat equation with Neumann boundary condition) Find the function MATH , MATH , MATH such that MATH for some functions MATH and MATH . The $U$ is assumed to be a bounded domain with a $C^{\infty}$ boundary. The MATH is the differentiation in the direction of the exterior normal to the boundary. The functions $f$ and $g$ are assumed to satisfy compatibility conditions motivationally similar to those of the proposition ( Parabolic regularity 2 ).




a. Weak formulation for Neumann boundary conditions. Natural and essential boundary conditions.

Notation. Index. Contents.


















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