The Hp-version Space-time Discontinuous Finite Element Methods For Parabolic Equations

The hp version discontinuous space-time finite element methods combines judiciously h version and p-refinement techniques.This kind of methods is highly adaptive,and suitable for dealing with complex discontinuous problems.The idea of combining the hp version discontinuous finite element methods with mixed finite element methods is considered for fourth order parabolic differential equations in this paper.For fourth order parabolic equations,the hp version mixed discontinuous space-time finite element scheme is constructed by lowering the order of the equation by mixed finite element.And the lowered equation is discretized by hp version discontinuous space-time finite element method,continuous in space but discontinuous in time.The stability,uniqueness and existence,exponential error estimates of the approximate solution are proved for linear problems.And then hp version discontinuous space-time finite element methods is used for a kind of Volterra integrodifferential parabolic equation with weakly singular kernel.The uniqueness of the approximate solution of the equation and the error estimate for time in L₂ norm and space in L₂ norm is obtained.