They may be referring to a 2D space in your model or to the use of plate elements. After all, you donвЂ™t know what someone means if they say 2D FEA. For this reason, Dirichlet boundary conditions are also called essential boundary conditions. Plate elements are often called 2D elements while solid elements are 3D elements. Additionally, the PeriodicBoundarењњondition has a third argument specifying the relation between the two parts of the boundary.ДЄ partial differential equation typically needs at least one Dirichlet boundary condition on some part of the region to be uniquely solvable. Specifying partial differential equations with boundary conditions.ДirichletCondition, NeumannValue and PeriodicBoundarењњondition all require a second argument that is a predicate describing the location on the boundary where the conditions/values are to be applied. System of coupled partial differential equation operators op j, Neumann boundary values О“ N j and Dirichlet and periodic boundary condition equations О“ D and О“ P DirichletCondition may also be given in a PDE equation as well. Making a NeumannValue part of a PDE equation solves this problem without ambiguity. It is not possible to derive (unambiguously) from the Neumann value with which PDE equation the value should be associated. One would like to be able to unambiguously specify any given Neumann value to any given single PDE of that system of PDEs. As such, it is a numerical rather than an analytical method. It is used mainly for problems for which no exact solution, expressible in some mathematical form, is available. Neumann values are mathematically tied to the PDE.ДЇor practical reasons, in NDSolve and related functions, NeumannValue needs to be given as a part of the equation. 1.1 What is finite element analysis (FEA) Finite element analysis is a method of solving, usually approximately, certain problems in engineering and science. Generalized Neumann values, on the other hand, are specified by giving a value, since the equation satisfied is implicit in the value. Dirichlet boundary conditions are specified as equations. They can be specified independently of the equation. In most cases, Dirichlet boundary conditions need not be associated with a particular equation. Other boundary conditions are conceivable, but currently not implemented. Periodic boundary conditions make the dependent variables behave according to a given relation between two distinct parts of the boundary. Instead of making use of integration by parts to obtain equation (11), the divergence theorem and Green's identities can also be used. Specifies the value of the boundary integral integrand (11) in the weak form and thus the name NeumannValue.

Finite element method example