A posteriori error estimates of the discontinuous Galerkin method for the heat conduction equation
Ivana Šebestová, V. Dolejší (2012)
Acta Universitatis Carolinae. Mathematica et Physica
Similarity:
Ivana Šebestová, V. Dolejší (2012)
Acta Universitatis Carolinae. Mathematica et Physica
Similarity:
Ivana Šebestová (2014)
Applications of Mathematics
Similarity:
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...
Andrea Toselli (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
Similarity:
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...