Discontinuous Mixed Covolume Methods for Parabolic Problems

A Mixed Covolume Method For The Pseudo-Parabolic Integro-Differential Equation On Triangular Grids

VARIATIONAL DISCRETIZATION AND MIXED METHODS FOR SEMILINEAR PARABOLIC OPTIMAL CONTROL PROBLEMS WITH INTEGRAL CONSTRAINT

The aim of this work is to investigate the variational discretization and mixed finite element methods for optimal control problem governed by semi linear parabolic equations with integral constraint. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is not discreted. Optimal error estimates in L2 are established for the state...

L Error Estimates and Superconvergence for Covolume or Finite Volume Element Methods

We consider convergence of the covolume or finite volume element solution to linear elliptic and parabolic problems. Error estimates and superconvergence results in the L norm, 2 p , are derived. We also show second-order convergence in the L norm between the covolume and the corresponding finite element solutions and between their gradients. The main tools used in this article are an extension...

Error Estimates in L, H and L∞ in Covolume Methods for Elliptic and Parabolic Problems: a Unified Approach

In this paper we consider covolume or finite volume element methods for variable coefficient elliptic and parabolic problems on convex smooth domains in the plane. We introduce a general approach for connecting these methods with finite element method analysis. This unified approach is used to prove known convergence results in the H1, L2 norms and new results in the max-norm. For the elliptic ...

Hp -version Discontinuous Galerkin Finite Element Methods for Semilinear Parabolic Problems

We consider the hp–version interior penalty discontinuous Galerkin finite element method (hp–DGFEM) for semilinear parabolic equations with mixed Dirichlet and Neumann boundary conditions. Our main concern is the error analysis of the hp–DGFEM on shape–regular spatial meshes. We derive error bounds under various hypotheses on the regularity of the solution, for both the symmetric and non–symmet...