A NEW CHARACTERISTIC EXPANDED MIXED METHOD FOR SOBOLEV EQUATION WITH CONVECTION TERM

Abstract

In this paper, a new numerical method based on a new expanded mixed scheme and the characteristic method is developed and discussed for Sobolev equation with convection term. The hyperbolic part [Formula: see text] is handled by the characteristic method and the diffusion term ∇ ⋅ (a(x, t)∇u+b(x, t)∇ut) is approximated by the new expanded mixed method, whose gradient belongs to the simple square integrable (L2(Ω))2 space instead of the classical H( div ; Ω) space. For a priori error estimates, some important lemmas based on the new expanded mixed projection are introduced. An optimal priori error estimates in L2-norm for the scalar unknown u and a priori error estimates in (L2)2-norm for its gradient λ, and its flux σ (the coefficients times the negative gradient) are derived. In particular, an optimal priori error estimate in H1-norm for the scalar unknown u is obtained.