Local Artificial Boundary Conditions for the Elliptic Boundary Value Problem in an Exterior Concave Region
This article employs local artificial boundary conditions for the approximation of the finite element method in solving the harmonic equation over an unbounded concave region.This approach transforms an unbounded problem into a more manageable bounded problem,paving a new avenue for tackling complex PDE issues.It not only alleviates the computational burden associated with boundarylessness but also enhances the efficiency and accuracy of numerical solutions.The paper further elucidates the variational formulation and numerical strategies for coupling natural boundary elements with finite elements for this equation,alongside an estimation of the approximation error.Numerical experiments are conducted to validate the efficacy and feasibility of the proposed method.
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