Analysis of a Finite Element Method pp 22-49 | Cite as

# Elliptic Problems — Forming the Algebraic Equations

Chapter

## Abstract

The form of the steady state PDE system solved by PDE/PROTRAN (Section 1.5), is: where R is a general two dimensional region and
\(\partial {R_1}\,and\,\partial {R_2}\) are disjoint parts of the boundary. The time dependent and eigenvalue problems will be studied in Chapters 4–6.

$$\begin{array}{*{20}{c}}
{0 = {A_x}(x,y,u,{u_x},{u_y}) + {B_y}(x,y,u,{u_x},{u_y}) + F(x,y,u,{u_x},{u_y})\,in\,R} \\
{u = FB(x,y)\,on\,\partial {R_1}} \\
{A{n_x} + B{n_y} = GB(x,y,u)\,on\,\partial {R_2}}
\end{array}\,$$

(2.1.1)

## Keywords

Piecewise Polynomial Numerical Integration Scheme Curve Triangle Galerkin Solution Piecewise Polynomial Approximation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## References

- 1.Strang, G., Fix, G., An Analysis of the Finite Element Method, Englewood Cliffs, N.J., Prentice-Hall, 1973.MATHGoogle Scholar
- 2.Burchard, H.G., “Splines (with Optimal Knots) are Better,” J. App. Anal. 3 (1974), pp 309–319.MathSciNetMATHCrossRefGoogle Scholar
- 3.Pereyra, V., Sewell, G., “Mesh Selection for Discrete Solution of Boundary Problems in Ordinary Differential Equations,” Numer. Math. 23, (1975) pp 26l–268.MathSciNetGoogle Scholar
- 4.Sewell, G., “Automatic Generation of Tri angulations for Piecewise Polynomial Approximation,” Ph.D. Thesis, Purdue University (1972).Google Scholar

## Copyright information

© Springer-Verlag New York Inc. 1985