1. Elliptic problems

Exa [EEHJ] p. 385 Stationary heat flow around a hot water pipe

[S-F]: Silvester-Ferrari: FEM for electrical eng.
CH 4 Triangular elements for the scalar Helmholtz equ. Includes details of higher order triangular elements.
Appl: High-order elements in waveguide analysis

2. Parabolic

Davies: The FEM: A first approach, Clarendon,Oxford

Use of Galerkin for time-dependent (and non-linear) problems 6.3 pp. 214 - One of two ways:

space-time triangulation
Space triangulation => system of ODE's.

See examples 6.4 and 6.5

PDEtool: 4-11 - 4-12

The latter way is used. System of ode's is solved using Matlab's ODE solvers. parabolic 5-43 - 5-44

[EEHJ] CH 16

The former (space-time triangulation) is used.

16.1 Maxwell's equ -> Heat equ
16.2.2 The fundamental sol.
16.4 A FEM for the heat equ

Problem p. 413

[WM] Wait-Mitchell: FEM anal. and appl.

Ch 5 p. 140 -> Time dependent probls Num. exa p. 156 Both ways treated, the latter: 5.3.5 1-step Galerkin: FEM in time p. 167 ->

1. Elliptic problems

2. Parabolic

Davies: The FEM: A first approach, Clarendon,Oxford

PDEtool: 4-11 - 4-12

[EEHJ] CH 16

[WM] Wait-Mitchell: FEM anal. and appl.

3. Hyperbolic

PDEtool: 4-13

[EEHJ] CH 17 The wave equ

[WM] p. 150-151 and ...

4. Nonlinear

[WM] p. 151-152

Other possibilities