An Introduction to the Finite Element Method for Differential Equations. Mohammad Asadzadeh

An Introduction to the Finite Element Method for Differential Equations

3. Exercise Section 3.8 Chapter 4. Exercise Section 4.3 Chapter 5. Exercise Section 5.4 Chapter 6. Exercise Section 6.7 Chapter 7. Exercise Section 7.2.3 Chapter 7. Exercise Section 7.3.3 Chapter 9. Poisson Equation. Exercise Section 9.4 Chapter 10. IBVPs: Exercise Section 10.3

15 Appendind B: Appendind BAlgorithms and Matlab CodesAlgorithms and Matlab Codes B.1 A Matlab Code to Compute the Mass Matrix M for a Nonuniform Mesh B.2 Matlab Routine to Compute the L2‐Projection B.3 A Matlab Routine Assembling the Stiffness Matrix B.4 A Matlab Routine to Assemble the Convection Matrix B.5 Matlab Routine for Forward‐, Backward‐Euler, and Crank–Nicolson B.6 A Matlab Routine for Mass‐Matrix in 2d B.7 A Matlab Routine for a Poisson Assembler in 2d

16 Appendix C: Appendix CSample AssignmentsSample Assignments C.1 Assignment 1 C.2 Assignment 2

17 Appendix D: Appendix DSymbolsSymbols D.1 Table of Symbols

18 Bibliography

19 Index

20 End User License Agreement

List of Tables

1 Chapter 8Table 8.1 Some one‐dimensional finite elements.Table 8.2 Some two‐dimensional finite elements with triangular elements.Table 8.3 Some two‐dimensional finite elements with quadrilateral elements.Table 8.4 Some three‐dimensional finite elements with tetrahedron elements.

List of Illustrations

1 Chapter 1Figure 1.1 Tricomi equation: an example of a variable coefficient classifica...Figure 1.2 Outward unit normal

at a point

.Figure 1.3 A heat‐conducting one‐dimensional wire.Figure 1.4 A vibrating string.

2 Chapter 2Figure 2.1 The hat function

over the interval

.Figure 2.2 Illustrating the existence of a unique solution for (V) and (M)....

3 Chapter 3Figure 3.1 Linear Lagrange basis functions for

.Figure 3.2 The linear interpolant

on a single interval.Figure 3.3 An example of a function in

.Figure 3.4 A general piecewise linear basis function

.Figure 3.5 A partition of

.Figure 3.6 Piecewise linear basis functions.Figure 3.7

and

Figure 3.8

and

.Figure 3.9 (a) Linear interpolation and (b) basis functions for

.Figure 3.10 Linear Lagrange basis functions for

.Figure 3.11 Piecewise linear interpolant

.Figure 3.12 Linear Lagrange basis functions for

on subinterval

.Figure 3.13 Example of a projection onto

.Figure 3.14 An example of a function

and its

projection

.Figure 3.15 Midpoint approximation

of the integral

.Figure 3.16 Trapezoidal approximation

of the integral

.Figure 3.17 Simpson's rule approximation

of the integral

.Figure 3.18 Identification of subintervals for composite Simpson's rule.Figure 3.19 Coefficients for composite Simpson's rule.

4 Chapter 5Figure 5.1 A partition of

into

nonuniform subintervals.Figure 5.2 The basis functions

.Figure 5.3

, and

.Figure

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