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On discontinuous Galerkin method and semiregular family of triangulations. (English) Zbl 1164.65499
Summary: Discretization of second order elliptic partial differential equations by discontinuous a Galerkin method often results in numerical schemes with penalties. We analyze these penalized schemes in the context of quite general triangular meshes satisfying only a semiregularity assumption. A new (modified) penalty term is presented and theoretical properties are proven together with illustrative numerical results.
MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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