We study existence, uniqueness, and a priori estimates for solutions for backward parabolic Ito equations in domains with boundary. The proofs are based duality between forward and backward equations. This duality is used also to establish that backward parabolic equations have some causality (more precisely, some anti-causality). AMS 1991 subject classification: Primary 60J55, 60J60, 60H10. Se...

Abstract. Convergence of a full discretization is shown for a general class of nonlinear parabolic November 10, 2011 problems. The numerical method combines the backward Euler method for the time discretization with a generalized internal approximation scheme for the spatial discretization. The governing monotone elliptic differential operator is described by a nonlinearity that may have anisot...

We consider the fictitious domain method with H1-penalty for a parabolic problem. First, the sharp error estimate for the H1penalty problem approximating the original problem is derived. Then, we present some regularity analysis and prior estimate to the H1-penalty problem. The finite element approximation is investigated for discrete problems of two types, “continuous-time” and “single-step ba...

The present essay scrutinizes the application of discrete mollification as a filtering procedure to solve a nonlinear backward inverse heat conduction problem in one dimensional space. These problems are seriously ill-posed. So, we combine discrete mollification and space marching method to address the ill-posedness of the proposed problem. Moreover, a proof of stability and<b...