On the control of pressure oscillation in bilinear-displacement constant-pressure element Original Research Article

Due to the singularity in the global pressure matrix equation, the bilinear-displacement constant-pressure element produces an uncontrollable checkerboard pattern in the pressure solution. Although the well-known penalty treatment in the pressure equation overcomes the singularity problem, it still produces oscillatory pressure under certain conditions. The proposed method employs a rank-one filtering operator in the pressure equation to filter out the checkerboard mode without affecting the non-checkerboarding pressure field. The numerical results suggest that the pressure oscillation in the penalty method and the rank-one filtering method is a result of the absence of the checkerboard mode. A pressure recovery procedure is then suggested to recover the appropriate checkerboard mode. Numerical results for both solid and fluid mechanics problems are included.