In this paper we study the finite element approximation for boundary control problems governed by semilinear elliptic equations. Optimal control problems are very important model in science and engineering numerical simulation. They have various physical backgrounds in many practical applications. Finite element approximation of optimal control problems plays a very important role in the numeri...

ERROR ESTIMATES OF A FIRST-ORDER LAGRANGE FINITE ELEMENT TECHNIQUE FOR NONLINEAR SCALAR CONSERVATION EQUATIONS∗ JEAN-LUC GUERMOND† AND BOJAN POPOV† Abstract. This paper establishes a O(h 1 4 ) error estimate in the L∞t (Lx)-norm for the approximation of scalar conservation equations using an explicit continuous finite element technique. A general a priori error estimate based on entropy inequal...

In this note, the missing error estimates in the L norm and in a new energy norm are established for a local-structure-preserving local discontinuous Galerkin method proposed in [F. Li and C.-W. Shu, Methods and Applications of Analysis, v13 (2006), pp.215-233] for the Laplace equation. With its distinctive feature in using harmonic polynomials as local approximations, the method has lower comp...

The Alekseev–Gröbner lemma is combined with the theory of modified equations to obtain an a priori estimate for the global error of numerical integrators. This estimate is correct up to a remainder term of order h, where h denotes the step size and p the order of the method. It is applied to a class of nonautonomous linear oscillatory equations, which includes the Airy equation, thereby improvi...

Galerkin approximations to solutions of a Cauchy-Dirichlet problem governed by the generalized porous medium equation