A DiscontinuoushpFinite Element Method for Diffusion Problems

摘要: We present an extension of the discontinuous Galerkin method which is applicable to numerical solution diffusion problems. The involves a weak imposition continuity conditions on values and fluxes across interelement boundaries. Within each element, arbitrary spectral approximations can be constructed with different orderspin element. demonstrate that elementwise conservative, property uncharacteristic high-order finite elements.For clarity, we focus model class linear second-order boundary value problems, developpriorierror estimates, convergence proofs, stability estimates. results experiments onh- andp-convergence rates for representative two-dimensional problems suggest robust capable delivering exponential convergence.