Error analysis for Laplace transform - finite element solution of hyperbolic equations
The finite element method with Laplace transform of the time variable for the hyperbolic problem \(u_{tt}+A(x)u(x,t)=q(x,t), (x,t)\in \Omega \times(0,\infty), A(x)=\sum_{| \alpha | =| \beta | =m}(-1)^{| \alpha |}D^{\alpha}a_{\alpha \beta}(x)D^{\beta}, \partial^ ju/\partial n^ j=0, (x,t)\in \partial \Omega \times(0,\infty),\) 0\(\leq j\leq m-1\), \(u(x,0)=u_ 0(x)\), \(u_ t(x,0)=u_ 1(x)\), \(x\in {\bar \Omega}\), is analysed. Error estimates in Hardy spaces \(L_ 2\quad(R^+,H^ m,\sigma), \sigma>0\), with weight \(e^{-2\sigma t}\) are derived.
scientific article; zbMATH DE number 3866526