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A space-time finite element method for the wave equation *
| Content Provider | Semantic Scholar |
|---|---|
| Author | French, Donald A. |
| Copyright Year | 2002 |
| Abstract | where n is a bounded open domain in R d with d ffi 1, 2 and T > 0. We have restricted our attention to a specific problem entirely to keep the presentation simple. Our results apply to considerably more general second-order hyperbolic problems. Typically an approximation to (1) is found by first discretizing in space to obtain the semidiscrete problem that consists of ordinary differential equations that depend on t. A standard finite difference technique is applied to obtain the full discretization. Lost in this approach is the ability to produce local mesh refinements in the space-time domain Q. For example, it would be difficult to accurately track a sharp wave front without taking small time steps. Another option involves converting the second-order equation into a first-order system of equations. However, new unknowns are introduced which lead to a larger discrete problem. Thus it is reasonable to try to approximate U directly through the form (1). (Note that there are several papers on space-time methods for first-order hyperbolic systems. See [1] for discussion and references). |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://web.mit.edu/ehliu/Public/ehliu/SpaceTime/French_1993_A_space-time_finite_element_method_for_the_wave_equation.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Approximation algorithm Discretization Finite difference Finite element method First-order predicate Large Paper |
| Content Type | Text |
| Resource Type | Article |
