This chapter is devoted to the approximation of time-dependent PDEs by finite elements. An exhaustive review of this vast subject goes beyond the scope of this book; therefore, we restrict ourselves to illustrating some important concepts. In particular, we emphasize the method of lines where the problem is first approximated in space, yielding a system of coupled ordinary differential equations, and then a time-marching algorithm is employed to construct the time-approximation.
KeywordsBilinear Form Parabolic Problem Finite Element Space Couple Ordinary Differential Equation Galerkin Solution
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