首页> 外文会议>International Conference on Large-Scale Scientific Computing(LSSC 2003); 20030604-20030608; Sozopol; BG >On the Computation of Blow-Up Solutions of Elliptic Equations with Semilinear Dynamical Boundary Conditions
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On the Computation of Blow-Up Solutions of Elliptic Equations with Semilinear Dynamical Boundary Conditions

机译:具有半线性动力边界条件的椭圆型方程爆破解的计算

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In this paper we study numerically blow-up solutions of elliptic equations with nonlinear dynamical boundary conditions. First, we formulate a result for blow-up, when dynamical boundary condition is posed on the part of the boundary. Next, by semidiscretization, we obtain a system of ordinary differential equations (ODEs), the solution of which also blows up. Under certain assumptions we prove that the numerical blow-up time converges to the corresponding real blow-up time, when the mesh size goes to zero. We investigate numerically the blow-up set (BUS) and the blow-up rate. Numerical experiments with local mesh refinement technique axe also discussed.
机译:在本文中,我们研究了具有非线性动态边界条件的椭圆型方程的数值爆破解。首先,当动态边界条件置于边界的一部分上时,我们为爆破制定公式。接下来,通过半离散化,我们获得了一个常微分方程组(ODE),其解也随之爆炸。在某些假设下,我们证明了当网格大小变为零时,数字爆炸时间会收敛到相应的实际爆炸时间。我们用数值方法研究爆破装置(BUS)和爆破率。还讨论了局部网格细化技术的数值实验。

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