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Robin boundary conditions are commonly used in solving Sturm–Liouville problems which appear in many contexts in science and engineering. In addition, the Robin boundary condition is a general form of the insulating boundary condition for convection–diffusion equations. Here, the convective and diffusive fluxes at the boundary sum to zero:
Showing wall boundary condition. The most common boundary that comes upon in confined fluid flow problems is the wall of the conduit. The appropriate requirement is called the no-slip boundary condition, wherein the normal component of velocity is fixed at zero, and the tangential component is set equal to the velocity of the wall. [1]
Boundary value problems are similar to initial value problems.A boundary value problem has conditions specified at the extremes ("boundaries") of the independent variable in the equation whereas an initial value problem has all of the conditions specified at the same value of the independent variable (and that value is at the lower boundary of the domain, thus the term "initial" value).
Given the orbital and solar conditions of early Mars, a greenhouse effect would have been necessary to increase surface temperatures at least 65 K in order for these surface features to have been carved by flowing water. [39] [40] A much denser, CO 2-dominated atmosphere has been proposed as a way to produce such a temperature increase. This ...
In finite-element analysis, the essential or Dirichlet boundary condition is defined by weighted-integral form of a differential equation. [2] The dependent unknown u in the same form as the weight function w appearing in the boundary expression is termed a primary variable , and its specification constitutes the essential or Dirichlet boundary ...
Since the problems in magnetostatics involve solving Laplace's equation or Poisson's equation for the magnetic scalar potential, the boundary condition is a Neumann condition. In spatial ecology , a Neumann boundary condition on a reaction–diffusion system , such as Fisher's equation , can be interpreted as a reflecting boundary, such that ...
An adjoint equation is a linear differential equation, usually derived from its primal equation using integration by parts.Gradient values with respect to a particular quantity of interest can be efficiently calculated by solving the adjoint equation.
In a weak formulation, equations or conditions are no longer required to hold absolutely (and this is not even well defined) and has instead weak solutions only with respect to certain "test vectors" or "test functions". In a strong formulation, the solution space is constructed such that these equations or conditions are already fulfilled.