InitializePDECoefficients::femcmsd

Details

This message is generated when the PDE has higher-than-second-order spatial derivatives.
Off[message] switches off the message; On[message] switches it on. For example: Off[InitializePDECoefficients::femcmsd].

Examples

Basic Examples (1)

In the case of a biharmonic equation, higher-than-second-order derivatives are present:

Wolfram Language code:

eq = Laplacian[Laplacian[w[x, y], {x, y}], {x, y}] == x * y;
bc = {w[0, y] == w[1, y] == w[x, 0] == w[x, 1] == 0, Derivative[2, 0][w][0, y] == Derivative[2, 0][w][1, y] == Derivative[0, 2][w][x, 0] == Derivative[0, 2][w][x, 1] == 0};
NDSolve[{eq, bc}, w, {x, 0, 1}, {y, 0, 1}]

The solution is to rewrite the equation as a system of two equations:

Wolfram Language code:

eqn = {Laplacian[u[x, y], {x, y}] == v[x, y], Laplacian[v[x, y], {x, y}] == x * y};
bcs = {u[0, y] == u[1, y] == u[x, 0] == u[x, 1] == 0, v[0, y] == v[1, y] == v[x, 0] == v[x, 1] == 0};
ufun = NDSolveValue[{eqn, bcs}, {u, v}, {x, 0, 1}, {y, 0, 1}][[1]]

Note that the derivative boundary conditions from the original problem are now Dirichlet conditions for the system of equations.

Plot the solution:

Wolfram Language code: Plot3D[ufun[x, y], {x, 0, 1}, {y, 0, 1}]