Abstract
A kind of boundary value problem about a second-order elliptic differential equation with variable coefficient is discussed indirectly by transforming it as the second kind of variational inequality form. Using regularization method, the variational inequality is formulated as an equal variational equation, which can be made discrete by the finite element method. Abstract error estimate and the error estimates of the approximation are derived under the energy norm and -norm.
Highlights
Suppose Ω ∈ Rn is a bounded open domain, Γ is the sufficiently smooth boundary of Ω, and n is the outward normal to
We had proven the variational inequality problem that is equal to problem (1), as follows:
2005, pp.121-124), this problem was formulated as an equal variational equation
Summary
Suppose Ω ∈ Rn is a bounded open domain, Γ is the sufficiently smooth boundary of Ω , and n is the outward normal to. We discuss the boundary value problem about a second-order elliptic type differential equation with variable coefficient as follows:. We had proven the variational inequality problem that is equal to problem (1), as follows:. The variational inequality exists only one solution. (Chen, 2008) Problem (2) originates from many physics and engineering reality. Using the regularization method (Chen, 2008), and making use of the differentiable function Ding, 2005, pp.121-124), this problem was formulated as an equal variational equation. Regularization about the variational inequality (2) and the process of solving the equal variational equation (Chen, 2008) will be iterated in the part briefly
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