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A discontinuous $$hp$$ finite element method for diffusion problems. (English) Zbl 0926.65109
This paper deals with a new type of the discontinuous Galerkin method that is applicable to a broad class of partial differential equations. The proposed method involves a weak imposition of continuity conditions on the solution values and on fluxes across interelement boundaries. The main features are a priori error estimations, convergence proofs, and stability estimates. The method is suited for an adaptive control of the error and can deliver high-order accuracy if the solution is smooth.

##### MSC:
 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs
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