Broken Reproducing Kernel Method For Elliptic Interface Problems

With the rapid development of science and technology,interface problems appear in many biochemical and material science simulations involving highly variable coefficients and singular source terms.Among many interface problems,elliptic interface problem has attracted much attention and been widely used.Because the elliptic interface problem involves the fields of environmental science,fluid mechanics,biomathematics and other disciplines,and the solution is also not smooth or discontinuous when the model equation derived from the actual problem is numerically solved,elliptic interface problem has attracted the interest of many scientific researchers.Thus,how to solve these problems by numerical simulation has become one of the most popular directions in engineering and scientific computing.Based on the one-dimensional elliptic interface problems and within the framework of reproducing kernel theory,the model equation is studied from the perspective of theoretical analysis and numerical simulation,and an effective numerical method is proposed.Firstly,according to the characteristics of elliptic equation,a new broken reproducing kernel space is constructed and the expression of reproducing kernel function is obtained.Secondly,a linear operator is defined and the operator equation equivalent to the original equation is obtained,and the approximate solution of the model is obtained by using the broken reproducing kernel method.Finally,the convergence of the proposed method is analyzed,and the effectiveness and superiority of the proposed method are illustrated by the algorithm program and numerical examples.