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- W63140170 abstract "Let us consider the following 1D problem: $$ left{ begin{gathered} {text{Find }}u:mathbb{R} times left] {0,T} right[ to mathbb{R}{text{ such that:}} hfill frac{{{partial ^2}u}}{{partial {t^2}}}left( {x,t} right) - {c^2}frac{{{partial ^2}u}}{{partial {x^2}}}left( {x,t} right) = 0{text{ in }}mathbb{R} times left] {0,T} right[, hfill uleft( {x,0} right) = {u_0}left( x right),frac{{partial u}}{{partial t}}left( {x,0} right) = {u_1}left( x right){text{ in }}mathbb{R}, hfill end{gathered} right. $$ ((11.1)) whose variational formulation is: $$ left{ begin{gathered} {text{Find }}uleft( {.,t} right) in {H^1}left( mathbb{R} right),t in left] {0,T} right[{text{ such that:}} hfill frac{{{d^2}}}{{d{t^2}}}int_mathbb{R} {uv{text{d}}x} + {c^2}int_mathbb{R} {frac{{partial u}}{{partial x}}frac{{partial v}}{{partial x}}} {text{d}}x = 0{text{ }}forall {text{v}} in {H^1}{text{ }}left( mathbb{R} right), hfill uleft( {x,0} right) = {u_0}left( x right),frac{{partial u}}{{partial t}}left( {x,0} right) = {u_1}left( x right){text{ in }}mathbb{R}. hfill end{gathered} right. $$ ((2.11)) In this section, we shall develop the semi-discretization in space of this problem, which is the main point of this study.KeywordsDispersion RelationDispersion CurveTaylor ExpansionFinite Difference MethodQuadrature RuleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves." @default.
- W63140170 created "2016-06-24" @default.
- W63140170 creator A5001661222 @default.
- W63140170 date "2002-01-01" @default.
- W63140170 modified "2023-09-27" @default.
- W63140170 title "Mass-Lumping in 1D" @default.
- W63140170 doi "https://doi.org/10.1007/978-3-662-04823-8_11" @default.
- W63140170 hasPublicationYear "2002" @default.
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