Field of Application

Primary Variable u

Material Constant k

Source Variable f

Secondary Variables d, du/dx, du/dy 

Heat Transfer

Temperature T

Conductivity k

Heat Source Q

Heat Flow q [comes from conduction k ¶T/¶n and convection h(T-Tµ)

Irrotational Flow of an Ideal Fluid

Stream Function y

Velocity Potential f

Density r

Density r

Mass Production s (normally zero)

Mass Production s (normally zero)

Velocities:

¶ y /¶x = -v;

¶ y /¶y = u

¶ f /¶x = -v;

¶ f /¶y = u

Groundwater Flow

Piezometric Head f

Permeability K

Recharge Q

Seepage: q = k¶ f/dn

Velocities:

u = -k¶ f/dx ,

v = -k¶ f/dy

Torsion of Members with Constant Cross-Section

Stress Function Y

k = 1

G = Shear Modulus

f = 2

q = angle of twist per unit length

Gqdf/dx = -syz

Gqdf/dx = -sxz

Electrostatics

Scalar Potential f

Dielectric Constant e

Charge Density r

Displacement Flux density Dn

Magnetostatics

Magnetic Potential f

Permeability m

Charge density r

Magnetic Flux density Bn

Transverse Deflection of Elastic Membranes

Transverse deflection u

Tension T in membrane

Transversely distributed Load

Normal force q