Dirichlet Neumann Algorithm For Elliptical Problem By Weak Galerkin Method

This paper aims to solve elliptic equation numerically using Dirichlet Neumann al-gorithm via weak Galerkin discretizition. Consider the following elliptic equations with boundary condition,where L is second order differential operator, L is defined as:Basic idea of weak Galerkin finite element method is to define a type of weak function v={v0, vb} and weak discrete gradient ▽d and weak discrete gradient ▽d、r to form the variation formular Weak gradient operator ▽d、r weaken the demand of the continuity of the trial space and test space that the standard finite element method requires, therefor the weak Galerkin can choose some totally discontinuous function to approximate the real solution.When we solving the partial differential equation, the domain area may be large and irregular, using the domain decomposition method allow us to decompose the original domain to several subdomains, then we can solve the problem in these smaller domain, this is much easier than the original problem, allowing employing different method on different subdomain and it is convenient to employ parallel algorithm.