Displaying similar documents to “ H P -finite element approximations on non-matching grids for partial differential equations with non-negative characteristic form”

A posteriori upper and lower error bound of the high-order discontinuous Galerkin method for the heat conduction equation

Ivana Šebestová (2014)

Applications of Mathematics

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We deal with the numerical solution of the nonstationary heat conduction equation with mixed Dirichlet/Neumann boundary conditions. The backward Euler method is employed for the time discretization and the interior penalty discontinuous Galerkin method for the space discretization. Assuming shape regularity, local quasi-uniformity, and transition conditions, we derive both a posteriori upper and lower error bounds. The analysis is based on the Helmholtz decomposition, the averaging interpolation...

-finite element approximations on non-matching grids for partial differential equations with non-negative characteristic form

Andrea Toselli (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We propose and analyze a domain decomposition method on non-matching grids for partial differential equations with non-negative characteristic form. No weak or strong continuity of the finite element functions, their normal derivatives, or linear combinations of the two is imposed across the boundaries of the subdomains. Instead, we employ suitable bilinear forms defined on the common interfaces, typical of discontinuous Galerkin approximations. We prove an error bound which is optimal...