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The standard conforming finite element methods on one type of highly nonuniform rectangular meshes are considered for solving the quasilinear singular perturbation problem -ϵ 2 ( u xx + u yy ) + ƒ( x , y ; u ) = 0. By using a special interpolation operator and the integral identity technique,...
Mortar elements form a family of special non-overlapping domain decomposition methods which allows the coupling of different triangulations across subdomain boundaries. We discuss and analyze a multilevel preconditioner for mortar finite elements on nonmatching triangulations. The analysis is...
In this paper local error estimates for mixed discontinuous Galerkin methods including the local discontinuous Galerkin method for solving second-order elliptic problems are established. Our result shows that the errors of both the vector and scalar solutions of the mixed DG methods in a local...
The boundary integral formulation for the Dirichlet boundary value problem is considered and the collocation boundary element method for the discretisation of the problem is used. In order to compute the entries of the matrices for several wave numbers, the inverse Fourier transform with respect...
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