论文标题
纯碰撞破裂方程的收敛和误差分析
Convergence and error analysis for pure collisional breakage equation
论文作者
论文摘要
颗粒过程中的碰撞断裂具有许多最近的好奇心。我们研究了纯碰撞破裂方程，该方程在本质上是非线性的，伴随着局部界限的断裂内核和碰撞内核。使用有限体积方案（FVS）离散连续方程，并分析近似溶液向精确溶液的弱收敛性，以实现非均匀的网格。分析的想法基于较弱的$ l^1 $紧凑性，并引入了适当的稳定条件。此外，当$ w_ {loc}^{1，\ infty} $ space以$ w_ {loc}^{1，\ infty} $ space中的内核时，为统一网格开发了理论错误分析。该方案被证明是一阶收敛性，对于三个核的测试示例进行数值验证。
Collisional breakage in the particulate process has a lot of recent curiosity. We study the pure collisional breakage equation which is nonlinear in nature accompanied by locally bounded breakage kernel and collision kernel. The continuous equation is discretized using a finite volume scheme (FVS) and the weak convergence of the approximated solution towards the exact solution is analyzed for non-uniform mesh. The idea of the analysis is based on the weak $L^1$ compactness and a suitable stable condition on time step is introduced. Furthermore, theoretical error analysis is developed for a uniform mesh when kernels are taken in $W_{loc}^{1,\infty}$ space. The scheme is shown to be first-order convergent which is verified numerically for three test examples of the kernels.
