The finite element method (FEM) is used to compute such approximations. The solution to the numerical model equations are, in turn, an approximation of the real solution to the PDEs. These discretization methods approximate the PDEs with numerical model equations, which can be solved using numerical methods. Instead, an approximation of the equations can be constructed, typically based upon different types of discretizations.
For the vast majority of geometries and problems, these PDEs cannot be solved with analytical methods.
The description of the laws of physics for space- and time-dependent problems are usually expressed in terms of partial differential equations (PDEs).
Physics, PDEs, and Numerical Modeling Finite Element Method An Introduction to the Finite Element Method
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