Singular and Dual Singular Functions for Partial Differential Equation with an Input Function in $H^1(\Omega)$
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In [6, 7] they introduced a new finite element method for ac- curate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with homogeneous boundary condi- tions, compute the finite element solutions using standard FEM and use the extraction formula to compute the stress intensity factor(s), then they posed new PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor(s), which converges with optimal speed. From the solution they could get an accu- rate solution just by adding the singular part. They considered a partial differential equation with the input function f ∈ L2(Ω). In this paper we consider a PDE with the input function f ∈ H1(Ω) and find the corresponding singular and dual singular functions. We also induce the corresponding extraction formula which are the basic element for the approach.
Abstract
In [6, 7] they introduced a new finite element method for ac- curate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with homogeneous boundary condi- tions, compute the finite element solutions using standard FEM and use the extraction formula to compute the stress intensity factor(s), then they posed new PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor(s), which converges with optimal speed. From the solution they could get an accu- rate solution just by adding the singular part. They considered a partial differential equation with the input function f ∈ L2(Ω). In this paper we consider a PDE with the input function f ∈ H1(Ω) and find the corresponding singular and dual singular functions. We also induce the corresponding extraction formula which are the basic element for the approach.
참고문헌 (9)
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- S. Kim, "Extraction formulas of stress intensity factors for the biharmonic equations containing crack singularities", Computers and Mathematics with Applications, 80, pp.1142~1163 (2020)
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