Geodesic
Finite element solution of a hyperbolic-parabolic problem
Applications of Mathematics, Tome 39 (1994) no. 3, pp. 215-239.

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Existence and finite element approximation of a hyperbolic-parabolic problem is studied. The original two-dimensional domain is approximated by a polygonal one (external approximations). The time discretization is obtained using Euler’s backward formula (Rothe’s method). Under certain smoothing assumptions on the data (see (2.6), (2.7)) the existence and uniqueness of the solution and the convergence of Rothe’s functions in the space $C(\overline{I},V)$ is proved.
DOI : 10.21136/AM.1994.134254
Classification : 65M12, 65M20, 65M60, 65N30
Keywords: Rothe's method; finite elements.; Euler’s backward formula; linear parabolic or hyperbolic equations; convergence 
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     author = {Hlavi\v{c}ka, Rudolf},
     title = {Finite element solution of a hyperbolic-parabolic problem},
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Hlavička, Rudolf. Finite element solution of a hyperbolic-parabolic problem. Applications of Mathematics, Tome 39 (1994) no. 3, pp. 215-239. doi : 10.21136/AM.1994.134254. http://geodesic.mathdoc.fr/articles/10.21136/AM.1994.134254/

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